Weak hypothesis generation apparatus and method, learning apparatus and method, detection apparatus and method, facial expression learning apparatus and method, facial expression recognition apparatus and method, and robot apparatus

ABSTRACT

A facial expression recognition system that uses a face detection apparatus realizing efficient learning and high-speed detection processing based on ensemble learning when detecting an area representing a detection target and that is robust against shifts of face position included in images and capable of highly accurate expression recognition, and a learning method for the system, are provided. When learning data to be used by the face detection apparatus by Adaboost, processing to select high-performance weak hypotheses from all weak hypotheses, then generate new weak hypotheses from these high-performance weak hypotheses on the basis of statistical characteristics, and select one weak hypothesis having the highest discrimination performance from these weak hypotheses, is repeated to sequentially generate a weak hypothesis, and a final hypothesis is thus acquired. In detection, using an abort threshold value that has been learned in advance, whether provided data can be obviously judged as a non-face is determined every time one weak hypothesis outputs the result of discrimination. If it can be judged so, processing is aborted. A predetermined Gabor filter is selected from the detected face image by an Adaboost technique, and a support vector for only a feature quantity extracted by the selected filter is learned, thus performing expression recognition.

This is a division of application Ser. No. 10/871,494, filed Jun. 17,2004, now U.S. Pat. No. 7,379,568, which is entitled to the priorityfiling dates of Japanese application 2003-417191 filed on Dec. 15, 2003and U.S. application Ser. No. 60/490,316 filed on Jul. 24, 2003, theentirety of which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a detection apparatus and method fordetecting, for example, a face image as a detection target image from animage in real time, a learning apparatus and method for learning data tobe used by the detection apparatus, a weak hypothesis generationapparatus and method for generating a weak hypothesis in learning, and arobot apparatus equipped with the detection apparatus. This inventionalso relates to a facial expression recognition apparatus and method forrecognizing a facial expression of a face image by detecting a specificexpression from the face image, a facial expression learning apparatusand method for learning data to be used by the facial expressionrecognition apparatus, and a robot apparatus equipped with the facialexpression recognition apparatus.

This application claims priority of U.S. Preliminary Application No.60/490,316, filed on Jul. 24, 2003 and Japanese Patent Application No.2003-417191, filed on Dec. 15, 2003, the entireties of which areincorporated by reference herein.

2. Description of the Related Art

Face to face communication is a real-time process operating at a timescale in the order of 40 milliseconds. The uncertainty of recognitionlevel at this time scale is extremely high, making it necessary forhumans and machines to rely on sensory rich perceptual primitives ratherthan slow symbolic inference processes. Thus, fulfilling the idea ofmachines that interact face to face with humans requires development ofrobust and real-time perceptual primitives.

Charles Darwin was one of the first scientists to recognize that facialexpression is one of the most powerful and immediate means for humanbeings to communicate their emotions, intentions, and opinions to eachother. In addition to providing information about affective state,facial expressions also provide information about cognitive state suchas interest, boredom, confusion, and stress, and conversational signalswith information about speech emphasis and syntax. Recently, a number ofgroundbreaking systems have appeared in the computer vision literaturefor facial expression recognition. (See, M. Pantic and J. M. Rothcrantz,Automatic analysis of facial expressions: State of the art, IEEETransactions on Pattern Analysis and Machine Intelligence, 22 (12):1424-1445, 2000.)

To recognize facial expressions in real time, first, it is necessary todetect a face area from an input image in real time. Conventionally,many face detection techniques using only variable density patterns ofimage signals without using any motion from complicated image sceneshave been proposed. For example, a face detector described in thefollowing non-patent reference 1 includes a cascade of classifiers, eachof which contains a filter such as Haar Basis function as adiscriminator. When generating the discriminator based on learning,high-speed learning is realized by using images called integral images,which will be described later, and rectangle features.

FIGS. 1A to 1D are schematic views showing rectangle features describedin the following non-patent reference 1. In the technique described innon-patent reference 1, as shown in FIGS. 1A to 1D, in input images 200Ato 200D, plural filters (also referred to as rectangle features) areprepared, each of which finds the sum of brightness values in adjacentrectangular boxes of the same size and outputs the difference betweenthe sum of brightness values in one or plural rectangular boxes and thesum of brightness values in the other rectangular boxes. For example, asshown in FIG. 1A, in the input image 200A, a filter 201A is shown, whichsubtracts the sum of brightness values in a shaded rectangular box201A-2 from the sum of brightness values in a rectangular box 201A-1 isshown. Such a filter including two rectangular boxes is calledtwo-rectangle feature. As shown in FIG. 1C, in the input image 200C, afilter 201C is shown, which is made up of three rectangular boxes 201C-1to 201C-3 formed by dividing one rectangular box into three boxes, andwhich subtracts the sum of brightness values in the shaded centralrectangular box 201C-2 from the sum of brightness values in therectangular boxes 201C-1l and 201C-3. Such a filter including threerectangular boxes is called three-rectangle feature. Moreover, as shownin FIG. 1D, in the input image 200D, a filter 201D is shown, which ismade up of four rectangular boxes 201D-1 to 201D-4 formed by verticallyand horizontally dividing one rectangular box into four boxes, and whichsubtracts the sum of brightness values in the shaded rectangular boxes201D-2 and 201D-4 from the sum of brightness values in the rectangularboxes 201D-1 and 201D-3. Such a filter including four rectangular boxesis called four-rectangle feature.

For example, judging a face image shown in FIG. 2 as a face image byusing rectangle features as described above will now be described. Atwo-rectangle feature (filter) 211B includes two rectangular boxes211B-1 and 211B-2 formed by vertically bisecting one rectangular box,and subtracts the sum of brightness values in the shaded rectangular box211B-1 from the sum of brightness values in the lower rectangular box211B-2. If the fact that the brightness value is lower in the eye areathan in the cheek area is utilized with respect to a human face image(detection target) 210, whether an input image is a face image or not(correct or incorrect) can be estimated with certain probability from anoutput value of the rectangle feature 211B.

The three-rectangle feature (filter) 211C is a filter that subtracts thesum of brightness values in the left and right rectangular boxes 211C-1and 211C-3 from the sum of brightness values in the central rectangularbox 211C-2. Similar to the above-described case, if the fact that thebrightness value is higher in the nose area than in the both of the eyeareas is utilized with respect to the human face image 210, whether aninput image is a face image or not can be judged to a certain degreefrom an output value of the rectangle feature 211C.

At the time of detection, in order to detect face areas of various sizesincluded in an input image, it is necessary to cut out areas of varioussizes (hereinafter referred to as search windows) for judgment. However,an input image made up of, for example, 320×240 pixels contains searchwindows of approximately 50,000 sizes, and arithmetic operations on allthese window sizes are very time-consuming.

Thus, according to non-patent reference 1, images called integral imagesare used. An integral image can be generated, for example, by carryingout an operation to add the pixel value of a position to the sum of thepixel value of the position that is immediately above and the pixelvalue of the position that is immediately left in the image,sequentially from the upper left part. It is an image in which the pixelvalue of an arbitrary position is the sum of brightness values in arectangular box that is upper left side of this position. If integralimages are found in advance, the sum of brightness values in arectangular box in an image can be calculated simply by adding orsubtracting the pixel values of the four corners of the rectangular box,and therefore the sum of brightness values in the rectangular box can becalculated at a high speed.

Moreover, in non-patent reference 1, a strong discrimination machine isused as a face detection apparatus, which uses many training data(learning samples), sequentially generates a discriminator based on theresult of calculation using integral images, and discriminates whetheran input image is a face image or not by weighted vote among outputsfrom many discriminators. FIG. 3 shows an essential part of the facedetection apparatus described in non-patent reference 1. As shown inFIG. 3, all window images (subwindows) 241 cut out from an input imageare inputted to the face detection apparatus. Then, one discriminatorsequentially outputs “correct” (=1) or “incorrect” (=−1). If the resultof weighted addition of these results in accordance with the reliability(lowness of error rate) of the discriminator is a positive value, it isassumed that a face exists in the window image and face detection iscarried out. Since the face detector includes many discriminators, it istime-consuming to cut out window images of difference sizes from theinput image and then take weighted vote among the results ofdiscrimination by all the discriminators with respect to all the windowimages. Thus, in non-patent reference 1, plural classifiers 240A, 240B,240C, . . . are prepared, each of which has plural discriminators, andthese plural classifiers are cascaded. Each of the classifiers 240A,240B, 240C, . . . once judges whether a window image is a face image ornot from its output. With respect to data 242A, 242B, 242C, . . . judgedas non-face images, judgment processing is interrupted at this point andonly data 2 judged as a face image by one classifier is supplied to thenext-stage classifier. The plural discriminators constituting thenext-stage classifier newly perform weighted addition and majority vote.As such processing is repeated, high-speed processing in face detectionis realized.

Non-Patent Reference 1: Paul Viola and Michael Jones, Robust real-timeobject detection, Technical Report CRL 2001/01, Cambridge ResearchLaboratory, 2001.

However, with respect to the rectangle features described in theabove-described non-patent reference 1, there are 160,000 or morepossible filters to be selected, depending on the number of pixelsconstituting the filters (sizes of filters) and the types of filterssuch as two-, three- and four-rectangle features, even if a target area(window image) is limited to, for example, a 24×24-pixel area.Therefore, in learning, an operation to select, for example, one filterthat provides a minimum error rate from the 160,000 or more filters, forexample, for several hundred labeled training data and thus generate adiscriminator must be repeated, for example, several hundred timescorresponding to the number of weighted votes. Therefore, an extremelylarge quantity of arithmetic operation is required and learningprocessing is very time-consuming.

Moreover, in the case of discriminating a face from an input image byusing a final hypothesis made up of many weak hypotheses acquired bylearning, as discrimination is made by a classifier made up of pluralweak hypotheses, as described above, the quantity of arithmeticoperation is reduced, compared with the case of making weighted voteamong sum values of all the weak hypotheses, and the discriminationprocessing speed can be improved. However, since each classifier needsto similarly take weighted vote, the processing is time-consuming.

SUMMARY OF THE INVENTION

In view of the foregoing status of the art, it is an object of thisinvention to provide a weak hypothesis generation apparatus and methodthat enable generation of weak hypotheses constituting a discriminatorat a high speed without lowering the discrimination performance whenlearning data to be used by the discriminator that discriminates whetherit is a detection target or not by ensemble learning.

It is another object of this invention to provide a detection apparatusand method that enable discrimination of a detection target at a highspeed without performing any redundant operation by sequentiallylearning output values of weak hypotheses for learning samples inadvance, when learning data to be used by a discriminator by boosting,and a learning apparatus and method that enable such high-speeddiscrimination.

It is still another object of this invention to provide a facialexpression recognition apparatus and method that are robust againstdeviation in face position contained in an image and that enableaccurate and quick recognition of facial expressions, and a facialexpression learning apparatus and method for learning data to be used bya facial expression recognition apparatus.

It is still another object of this invention to provide a robotapparatus equipped with a detection apparatus capable of detecting adetection target accurately in real time from an input image, and arobot apparatus equipped with a facial expression recognition apparatuscapable of recognizing expressions of face images accurately at a highspeed.

A weak hypothesis generation apparatus according to this invention isadapted for generating a weak hypothesis for estimating whether provideddata is a detection target or not by using a data set including plurallearning samples, each of which has been labeled as a detection targetor non-detection target. The weak hypothesis generation apparatusincludes: a selection unit for selecting a part of plural hypotheses andselecting one or plural weak hypotheses having higher estimationperformance than others with respect to the data set of the selectedpart of the hypotheses, as high-performance weak hypotheses; a new weakhypothesis generation unit for generating one or more new weakhypotheses formed by adding a predetermined modification to thehigh-performance weak hypotheses, as new weak hypotheses; and a weakhypothesis selection unit for selecting one weak hypothesis having thehighest estimation performance with respect to the data set, from thehigh-performance weak hypotheses and the new weak hypotheses.

In this invention, using a part of all the selectable weak hypothesesinstead of all the selectable weak hypotheses, one or plural weakhypotheses having high discrimination performance (estimationperformance), that is, having a low error rate, are selected ashigh-performance weak hypotheses. Then, a new weak hypothesis orhypotheses formed by adding a predetermined modification to the selectedhigh-performance weak hypotheses are generated, and a weak hypothesishaving the highest discrimination performance is selected from these,thus generating a weak hypothesis. This enables reduction in thequantity of arithmetic operation without lowering the accuracy, comparedwith the case of selecting a weak hypothesis of the highestdiscrimination performance from all the selectable weak hypotheses.

The new weak hypothesis generation unit can generate new weak hypothesesfrom the high-performance weak hypotheses on the basis of statisticalcharacteristics of the detection target. For example, in the case ofdetecting a human face, it generates new weak hypotheses by utilizingleft-and-right symmetry of the face. This enables generation of new weakhypotheses that are expected to have a low estimation error rate andhigh performance equivalent to those of the high-performance weakhypotheses. As a weak hypothesis is selected from these weak hypothesesby the weak hypothesis selection unit, a weak hypothesis having highdiscrimination performance can be generated while reducing the quantityof arithmetic operation compared with the case of selecting one of allthe selectable weak hypotheses.

Moreover, data weighting is set for each learning sample of the dataset, and the estimation performance with respect to the data set can becalculated on the basis of the data weighting set for each learningsample of the data set. An apparatus that generates a weak hypothesisused for boosting can be realized.

Furthermore, the apparatus also has a data weighting update unit forupdating the data weighting of each of the learning samples on the basisof the estimation performance with respect to the data set, of the weakhypothesis selected by the weak hypothesis selection unit. Every timethe data weighting is updated by the data weighting update unit, theprocessing to generate a weak hypothesis by selecting one of the pluralweak hypothesis can be repeated. This enables construction of a learningapparatus that updates the distribution of the data weighting every timea weak hypothesis is generated and learns a final hypothesis by boostingin which a weak hypothesis is generated in accordance with the updateddistribution of the data weighting.

The data weighting update unit updates the data weighting in such amanner that the data weighting of a learning sample on which theestimation value outputted by the weak hypothesis is incorrect becomesrelatively larger than the data weighting of a learning sample on whichthe estimation value is correct. Thus, it is possible to sequentiallygenerate a weak hypothesis whereby a learning sample that is hard todiscriminate and has large data weighting becomes correct.

Moreover, the weak hypothesis can deterministically output theestimation value with respect to provided data, and learning inaccordance with an algorithm such as Adaboost can be carried out. If theestimation value with respect to provided data is outputtedprobabilistically, the estimation performance can be improved further.

Furthermore, the data set includes a variable density image representingthe detection target and a variable density image representing thenon-detection target. The weak hypothesis may estimate whether avariable density image provided as an input is a detection target or noton the basis of the difference between the sum of brightness values inone or plural rectangular boxes and the sum of brightness values in theother rectangular boxes in a group of two or more rectangular boxescontained in the variable density image. If integral images, which willbe described later, are used, the feature quantity of the rectanglefeature can be calculated at a higher speed.

Another weak hypothesis generation apparatus according to this inventionis adapted for generating a weak hypothesis for estimating whetherprovided data is a detection target or not by using a data set includingplural learning samples each of which has been labeled as a detectiontarget or non-detection target. The weak hypothesis generation apparatusincludes: a selection unit for selecting a part of plural weakhypotheses; a new weak hypothesis generation unit for generating one ormore new weak hypotheses formed by adding a predetermined modificationto the part of the weak hypotheses selected by the selection unit, asnew weak hypotheses; and a weak hypothesis selection unit for selectingone weak hypothesis having the highest estimation performance withrespect to the data set, from the part of the weak hypotheses selectedby the selection unit and the new weak hypotheses.

In this invention, a part of many selectable weak hypotheses is randomlyselected, and one weak hypothesis having high discrimination performanceis selected from the selected part of the weak hypotheses and generatednew weak hypotheses, thus generating a weak hypothesis. Therefore, it ispossible to generate a weak hypothesis having higher performance than inthe case of generating a weak hypothesis by randomly selecting a part ofhypotheses and selecting one weak hypothesis of high performance fromthese.

A learning apparatus according to this invention is adapted for learningdata to be used by a detection apparatus, the detection apparatus beingadapted for judging whether provided data is a detection target or notby using a data set including plural learning samples each of which hasbeen labeled as a detection target or non-detection target. The learningapparatus includes: a weak hypothesis selection unit for repeatingprocessing to select one weak hypothesis from plural weak hypotheses forestimating whether provided data is a detection target or not; areliability calculation unit for, every time a weak hypothesis isselected by the weak hypothesis selection unit, calculating reliabilityof the weak hypothesis on the basis of the result of estimation of theselected weak hypothesis with respect to the data set; and a thresholdvalue learning unit for calculating and adding the product of the resultof estimation of the weak hypothesis with respect to the data set andthe reliability of the weak hypothesis every time a weak hypothesis isselected by the weak hypothesis selection unit, and learning an abortthreshold value for aborting the processing by the detection apparatusto judge whether the provided data is a detection target or not on thebasis of the result of the addition.

In this invention, for example, in the case where there are much morenon-detection targets than detection targets included in provided data,the abort threshold value that has been learned in advance is used toabort detection processing when it can be judged that the provided datais obviously a non-detection target, or conversely, to abort detectionprocessing when it can be judged that the provided data is obviously adetection target. Thus, the detection apparatus that performs thedetection processing very efficiently can be provided.

The threshold value learning unit can learn the abort threshold value onthe basis of the result of addition of the product of the result ofestimation of the weak hypothesis with respect to positive data labeledas the detection target, of the data set, and the reliability of theweak hypothesis, calculated and added every time a weak hypothesis isselected by the weak hypothesis selection unit. For example, it canstore a smaller one of a minimum value of the result of addition withrespect to the positive data and a discrimination boundary value, as theabort threshold value, every time the weak hypothesis is selected. Thisenables provision of a detection apparatus that aborts processing,assuming that obviously non-detection target data is inputted when theresult of addition is smaller than the minimum possible value of thepositive data.

Moreover, the threshold value learning unit can learn the abortthreshold value on the basis of the result of addition of the product ofthe result of estimation of the weak hypothesis with respect to negativedata labeled as the non-detection target, of the data set, and thereliability of the weak hypothesis, calculated and added every time aweak hypothesis is selected by the weak hypothesis selection unit. Forexample, it can store a larger one of a maximum value of the result ofcalculation with respect to the negative data and a discriminationboundary value, as the abort threshold value, every time the weakhypothesis is selected. This enables provision of a detection apparatusthat aborts processing, assuming that clearly detection target data isinputted when the result of addition is larger than the maximum possiblevalue of the negative data.

A detection apparatus according to this invention is adapted fordetecting a detection target by discriminating whether provided data isa detection target or not. The detection apparatus includes: anestimation result output unit including plural weak hypotheses; and adiscrimination unit for discriminating whether the provided data is adetection target or not on the basis of the result of output of theestimation result output unit; wherein the estimation result output unitestimates and outputs whether the provided data is a detection target ornot for each weak hypothesis on the basis of a feature quantity that hasbeen learned in advance, and the discrimination unit has an abort unitfor adding the product of the result of estimation of a weak hypothesisand reliability that has been learned in advance on the basis ofestimation performance of the weak hypothesis, every time one hypothesisoutputs the result of estimation, and deciding whether or not to abortprocessing by the estimation result output unit on the basis of theresult of the addition.

In this invention, as an abort threshold value that has been learned inadvance and the product of the result of estimation and reliability ofthe weak hypothesis are compared with each other every time one weakhypothesis outputs the result of estimation, whether or not to abortcalculation of the weak hypothesis can be decided. Therefore, redundantcalculation can be omitted and detection processing can be performed ata higher speed.

The detection target can be a face image. In this case, a system can beprovided that has a face feature extraction unit for filtering, with aGabor filter, a face image detected as the detection target by thediscrimination unit and thus extracting a face feature, and a facialexpression recognition unit for recognizing an expression of theprovided face image on the basis of the face feature, and that detects aface image at a high speed and recognize its expression, therebyrecognizing an expression of a human being in real time from dynamicimages such as video images.

A facial expression learning apparatus according to this invention isadapted for learning data to be used by a facial expression recognitionapparatus, the facial expression recognition apparatus being adapted forrecognizing an expression of a provided face image by using anexpression learning data set including plural face images representingspecific expressions as recognition targets and plural face imagesrepresenting expressions different from the specific expressions. Thefacial expression learning apparatus includes a facial expressionlearning unit for learning data to be used by the facial expressionrecognition apparatus, the facial expression recognition apparatusidentifying the face images representing the specific expressions fromprovided face images on the basis of the face feature extracted from theexpression learning data set by using a Gabor filter.

In this invention, as an output of the Gabor filter that filters aninput image by using plural filters having direction selectivity anddifferent frequency components is used as a feature quantity, a featurequantity that is less affected by a shift of the image or environmentalchanges can be extracted. As data for an expression identifier thatidentifies specific expression is learned by using expression learningsamples labeled with each expression for a desired number of expressionsto be identified, a facial expression recognition apparatus capable ofrecognizing an arbitrary expression form a provided face image can beprovided.

The expression learning unit can learn a support vector for identifyinga face image representing the specific expression on the basis of theface feature extracted from the expression learning data set by usingthe Gabor filter. By a support vector machine that once reflects theextracted face feature onto a nonlinear feature space and finds ahyperspace separating in this feature space to identify a face and anon-face object, a facial expression recognition apparatus capable ofrecognizing a desired expression with high accuracy can be provided.

Moreover, the expression learning unit has a weak hypothesis generationunit for repeating processing to generate a weak hypothesis forestimating whether a provided face image is of the specific expressionor not on the basis of the result of filtering by one Gabor filterselected from plural Gabor filters, a reliability calculation unit forcalculating reliability of the weak hypothesis generated by the weakhypothesis generation unit on the basis of estimation performance of theweak hypothesis with respect to the expression learning data set, and adata weighting update unit for updating data weighting set for theexpression learning data set on the basis of the reliability. The weakhypothesis generation unit can repeat the processing to generate theweak hypothesis while selecting one Gabor filter having the highestestimation performance with respect to the expression learning data setevery time the data weighting is updated. One of outputs of the pluralGabor filters decided in accordance with the frequencies and directionsof the Gabor filters and pixel positions in the learning sample isselected to generate a weak hypothesis, and as this is repeated, datafor an identifier to provide a final hypothesis can be learned.

Furthermore, the expression learning unit has a weak hypothesisgeneration unit for repeating processing to generate a weak hypothesisfor estimating whether a provided face image is of the specificexpression or not on the basis of the result of filtering by one Gaborfilter selected from plural Gabor filters, a reliability calculationunit for calculating reliability of the weak hypothesis generated by theweak hypothesis generation unit on the basis of estimation performanceof the weak hypothesis with respect to the expression learning data set,a data weighting update unit for updating data weighting set for theexpression learning data set on the basis of the reliability, and asupport vector learning unit for learning a support vector foridentifying a face image representing the specific expression on thebasis of the face feature extracted form the expression learning dataset by a predetermined Gabor filter. The weak hypothesis generation unitrepeats the processing to generate the weak hypothesis while selectingone Gabor filter having the highest estimation performance with respectto the expression learning data set every time the data weighting isupdated. The support vector learning unit extracts the face feature byusing the Gabor filter selected by the weak hypothesis generated by theweak hypothesis generation unit, and thus can learn the support vector.Outputs of all the Gabor filters decided in accordance with thefrequencies and directions of the Gabor filters and pixel positions in alearning sample are used as weak hypotheses, and several weak hypotheseshaving high discrimination performance are selected form these. As thesupport vector is learned by using these selected weak hypotheses as thefeature quantity, the dimension of the vector is lowered and thequantity of arithmetic operation at the time of learning is thus reducedsignificantly. Also, as ensemble learning and a support vector machineare combined, a facial expression recognition apparatus having highergeneral-purpose capability can be provided.

A facial expression recognition apparatus according to this inventionincludes: a face feature extraction unit for filtering a provided faceimage by using a Gabor filter and extracting a face feature; and anexpression recognition unit for recognizing an expression of theprovided face image on the basis of the face feature.

In this invention, since a feature quantity is extracted from a providedface image by a Gabor filter that is robust against a shift of theimage, the result of recognition that is robust against environmentchanges can be acquired. The expression recognition unit can be formedby an expression identifier having its data learned by SVM or boostingor by a combination of these. An expression can be recognized from aface image very accurately.

A robot apparatus according to this invention is an autonomously actingrobot apparatus. The robot apparatus includes: an image pickup unit forpicking up an image of its surroundings; a cut-out unit for cutting outa window image of an arbitrary size from the image picked up by theimage pickup unit; and a detection apparatus for detecting whether thewindow image is an image representing a detection target or not. Thedetection apparatus has an estimation result output unit includingplural weak hypotheses, and a discrimination unit for discriminatingwhether the window image is an image representing a detection target ornot on the basis of the result of estimation outputted from theestimation result output unit. The estimation result output unitestimates and outputs whether the provided data is a detection target ornot for each weak hypothesis on the basis of a feature quantity that hasbeen learned in advance. The discrimination unit has an abort unit foradding the product of the result of estimation of a weak hypothesis andreliability learned on the basis of estimation performance of the weakhypothesis every time one weak hypothesis outputs the result ofestimation, and deciding whether or not to abort processing by theestimation result output unit on the basis of the result of theaddition.

In this invention, using an abort threshold value when detecting adetection target from an input image, detection processing to detectwhether a provided image is a detection target or not can be omitted,and a target object can be detection in real time from an inputtedstatic image or dynamic image.

A robot apparatus according to this invention is an autonomously actingrobot apparatus. The robot apparatus includes: an image pickup unit forpicking up an image of its surroundings; a face image detectionapparatus for detecting a predetermined area as a face image from theimage picked up by the image pickup unit; and a facial expressionrecognition apparatus for recognizing an expression of the face image.The facial expression recognition apparatus has a face featureextraction unit for filtering the face image detected by the face imagedetection apparatus by using a Gabor filter and thus extracting a facefeature, and an expression recognition unit for recognizing anexpression of the provided face image on the basis of the face feature.

In this invention, even an autonomously acting robot apparatus canaccurately recognize an expression from a face image by using a featurequantity that is robust against environmental changes.

With the weak hypothesis generation apparatus and method according tothis invention, when estimating whether provided data is a detectiontarget or not by using a data set including plural learning samples eachof which has been labeled as a detection target or non-detection target,first, a part of plural weak hypotheses is selected and one or pluralweak hypotheses having higher estimation performance with respect to thedata set, of the selected part of weak hypotheses, are selected ashigh-performance weak hypotheses. Next, one or more new weak hypothesesformed by adding a predetermined modification to the high-performanceweak hypotheses are generated as new weak hypotheses. Then, one weakhypothesis having the highest estimation performance with respect to thedata set is selected from the high-performance weak hypotheses and thenew weak hypotheses, thus generating a weak hypothesis. By thusselecting weak hypotheses of high discrimination performance from a partof all the selectable weak hypotheses, generating new weak hypotheseswith a predetermined modification from the selected high-performanceweak hypotheses, and employing a weak hypothesis having the highestdiscrimination performance from these, it is possible to significantlyreduce the quantity of arithmetic operation without lowering theaccuracy compared with the case of selecting a weak hypothesis havinghigh discrimination performance from all the selectable weak hypotheses.As a weak hypothesis is thus generated at a high speed, data for adiscriminator to provide a final hypothesis can be learned at a highspeed and a learning machine with high accuracy can be provided.

With another weak hypothesis generation apparatus and method accordingto this invention, a part of plural weak hypotheses is selected and oneor more new weak hypotheses formed by adding a predeterminedmodification to the selected part of weak hypotheses are generated. Ofthese weak hypotheses, a weak hypothesis having a minimum error ratewith respect to a learning data set is selected, thus generating a weakhypothesis. Therefore, a weak hypothesis can be generated at a highspeed, compared with the case of selecting a weak hypothesis having highdiscrimination performance from all the selectable weak hypotheses, anda weak hypothesis having higher performance than a weak hypothesisselected from a part of the weak hypotheses can be generated.

With the learning apparatus and method according to this invention, datafor a detection apparatus that judges whether a provided data is adetection target or not is learned by using a data set including plurallearning samples each of which has been labeled as a detection target ornon-detection target. In learning, processing to select one of pluralweak hypotheses for estimating whether provided data is a detectiontarget or not is repeated. In this processing, every time a weakhypothesis is selected, reliability of the weak hypothesis is calculatedon the basis of the result of estimation of the selected weak hypothesiswith respect to the data set, and the product of the result ofestimation of the weak hypothesis with respect to the data set and thereliability of the weak hypothesis is calculated and added every time aweak hypothesis is selected. Then, an abort threshold value for abortingthe processing by the detection apparatus to judge whether the provideddata is a detection target or not on the basis of the result of additionis learned. Therefore, in detecting a target object, it is possible toabort the detection processing on the basis of a judgment that aprovided image is obviously not a detection target or to abort thedetection processing on the basis of a judgment that a provided image isobviously a detection target in accordance with the abort thresholdvalue. Redundant processing can be omitted and a detection apparatuscapable of performing detection processing at a high speed can beprovided.

With the detection apparatus and method according to this invention,when detecting a detection target by discriminating whether provideddata is a detection target or not, whether or not provided data is adetection target or not is estimated and outputted for each weakhypothesis on the basis of a feature quantity that has been learned inadvance with respect to plural weak hypotheses, and whether the provideddata is a detection target or not is discriminated on the basis of theresult of output. In this case, the product of the result of estimationof the weak hypothesis and reliability that has been learned in advanceon the basis of the estimation performance of the weak hypothesis isadded every time one weak hypothesis outputs the result of estimation,and whether or not to abort the estimation processing of the weakhypothesis is decided on the basis of the result of addition. Therefore,for example, in the case where there are much more non-detection targetsthan detection targets, whether or not provided data is obviously anon-detection target is judged in accordance with an abort thresholdvalue that has been learned in advance. When it can be judged that theprovided data is obviously a non-detection target, the detectionprocessing can be aborted. Thus, the detection processing can beperformed very efficiently and a higher speed. Moreover, if a face imageis detected as a detection target, a face can be detected from a dynamicimage or the like in real time. Combined with a facial expressionrecognition apparatus that recognizes an expression of this face image,it is possible to recognize an expression of a human being from an inputimage in real time.

With the facial expression learning apparatus and method according tothis invention, data for a facial expression recognition apparatus thatrecognizes an expression of a provided face image is learned by using anexpression learning data set including plural face images representingspecific expressions as recognition targets and plural face imagesrepresenting expressions different from the specific expressions. Inthis case, face features are learned for the facial expressionrecognition apparatus to identify a face image representing the specificexpressions from provided face images on the basis of face featuresextracted from the expression learning data set by a Gabor filter. Sincean output of the Gabor filter is used as a feature quantity, theapparatus is robust against a shift of the image. As data for anexpression identifier that identifies a specific expression of anidentification target is learned for a desired number of expressions byusing expression learning samples labeled for each expression, a facialexpression recognition apparatus that recognizes a desired expressionfrom a provided face image can be provided. Moreover, if a supportvector for identifying a specific expression is learned, the expressionidentifier can be a support vector machine and a facial expressionrecognition apparatus with very high accuracy can be provided.Furthermore, if ensemble learning is performed by a technique such asboosting using an expression identifier that identifies a specificexpression as a final hypothesis, a facial expression recognitionapparatus capable of high-speed operation with high accuracy can beprovided. As the dimension of a vector to be learned is lowered byperforming feature selection for learning a support vector by boosting,it is possible to realize high-speed operation at the time of learningand to provide a facial expression identification apparatus thatoperates at a high-speed and has very high general-purpose performance.

With the facial expression recognition apparatus and method according tothis invention, a provided face image is filtered by a Gabor filter toextract a face feature, and an expression of the provided face image isrecognized on the basis of this face feature. Therefore, a featurequantity robust against environmental changes can be extracted and afacial expression can be recognized accurately.

With the robot apparatus according to this invention, when equipped witha detection apparatus capable of high-speed detection processing or afacial expression recognition apparatus that recognizes an expression ofa face image as described above, a robot apparatus of excellententertainment quality that can recognize an expression of a human beingin real time and present an action in accordance with the emotion of theuser can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A to 1D are schematic views showing rectangle features describedin non-patent reference 1.

FIG. 2 is a view described in non-patent reference 1 for explaining aface image judgment method using rectangle features.

FIG. 3 is a schematic view showing a part of cascaded discriminatorsdescribed in non-patent reference 1.

FIG. 4 is a block diagram showing a facial expression recognition systemaccording to an embodiment of this invention.

FIG. 5 is a block diagram schematically showing a learner acquired byensemble learning.

FIG. 6 is a schematic view showing rectangle features used in a facedetection apparatus of the facial expression recognition systemaccording to an embodiment of this invention.

FIG. 7 is a view for explaining a method for detecting a face imageusing the rectangle features.

FIG. 8A is a schematic view showing an integral image. FIG. 8B is a viewfor explaining a method for calculating the sum of brightness values ina rectangular box, using an integral image.

FIG. 9 is a graph with the horizontal axis representing the number ofweak hypotheses t and the vertical axis representing a sum valueobtained by multiplying weighting to outputs of the weak hypotheses andadding them, in which changes of the sum value in accordance withwhether an inputted image is a face image or not and an abort thresholdvalue are shown.

FIG. 10 is a functional block diagram showing a learner in the facedetection apparatus of the facial expression recognition systemaccording to an embodiment of this invention.

FIG. 11 is a flowchart showing a learning method for a discriminator inthe face detection apparatus of the facial expression recognition systemaccording to an embodiment of this invention.

FIG. 12 is a flowchart showing a weak hypothesis generation method inthe face detection apparatus of the facial expression recognition systemaccording to an embodiment of this invention.

FIG. 13 is a schematic view showing examples of filters to be generatedin a learning process for the face detection apparatus of the facialexpression recognition system according to an embodiment of thisinvention.

FIG. 14 is a flowchart showing a face detection method in the facedetection apparatus of the facial expression recognition systemaccording to an embodiment of this invention.

FIG. 15 is a functional block diagram showing a facial expressionrecognition apparatus 20 of the facial expression recognition systemaccording to an embodiment of this invention.

FIG. 16 is a flowchart showing a first learning method for the facialexpression recognition apparatus of the facial expression recognitionsystem according to an embodiment of this invention.

FIG. 17 is a flowchart showing a second learning method for the facialexpression recognition apparatus of the facial expression recognitionsystem according to an embodiment of this invention.

FIG. 18 is a graph with the horizontal axis representing output of thej-th Gabor filter and the vertical axis representing the number ofpositive data p or negative data n in the output of the j-th Gaborfilter.

FIG. 19 is a flowchart showing a third learning method for the facialexpression recognition apparatus of the facial expression recognitionsystem according to an embodiment of this invention.

FIG. 20A is a view showing Gabor filters of difference frequencycomponents. FIG. 20B is a view showing eight directions of a Gaborfilter.

FIG. 21 is a view showing an identification plane of soft margin SVM.

FIG. 22 is a perspective view showing an outlook of a robot apparatusaccording to an embodiment of this invention.

FIG. 23 is a view schematically showing a joint degree-of-freedomstructure of the robot apparatus.

FIG. 24 is a schematic view showing a control system structure of therobot apparatus.

FIG. 25A is a view showing a first filter selected by a face detectionapparatus in an example of this invention. FIG. 25B is a view showing anactual-value output (or tuning curve) of a weak learner with respect toall the samples acquired by the filter shown in FIG. 25A, that is, anaverage face.

FIG. 26A is a view showing a second filter selected by the facedetection apparatus in an example of this invention. FIG. 26B is a viewshowing an actual-value output (or tuning curve) of a weak learner withrespect to all the samples acquired by the filter shown in FIG. 25A,that is, an average face.

FIG. 27A is a graph showing an output of one emotion classifier duringAdaboost training in an example of this invention. FIG. 27B is a graphshowing a generalization error as a function of the number of featuresselected by Adaboost in the example of this invention.

FIG. 28 is a view showing first five Gabor filers (Gabor features)selected for each emotion in an example of this invention.

FIG. 29 is a graph showing wavelength distribution of a feature selectedby Adaboost with respect to five frequencies that are used.

FIGS. 30A and 30B are graphs showing the results of output by anexpression identifier that identifies emotions of “anger” and “disgust”,respectively, in an example of this invention.

FIG. 31 is a view showing an exemplary output of an emotion mirrorapparatus utilizing the facial expression recognition system in anexample of this invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An embodiment of this invention will now be described in detail withreference to the drawings. In this embodiment, this invention is appliedto a facial expression recognition system including a detectionapparatus that detects a face image as a detection target from aninputted image or video and a facial expression recognition apparatusthat recognizes an expression of the face image detected by thedetection apparatus.

This facial expression recognition system can detect a face image from avideo and can carry out user-independent and fully automatic real-timerecognition of basic emotional expressions. Moreover, this facialexpression recognition system automatically detects frontal faces invideo streams and codes them to identify plural emotions such asneutral, anger, disgust, fear, joy, sadness, and surprise.

Data for the detection apparatus has been learned by ensemble learningusing a data set including plural face images as learning samplesrepresenting detection targets and plural non-face images as learningsamples representing non-detection targets. The facial expressionrecognition apparatus is an apparatus that identifies plural facialexpressions by support vector machines (SVM), or learners acquired byensemble learning, or a combination of these, using an output of a Gaborfilter of the face image detected by the detection apparatus as afeature quantity. That is, data for both of these apparatuses havemachine-learned by using learning samples called teacher data ortraining data.

First, prior to the explanation of this embodiment, ensemble learningwill be described, which is one of learning algorithms used in thisembodiment. Ensemble learning is described, for example, in Hideki Ado,et al., “Statistics of pattern recognition and learning: new conceptsand techniques”, Iwanami.

A hypothesis deterministically or probabilistically predicts oneresponse y to an input x. When a hypothesis is expressed by a parameterθ, it is described as y=h(x,θ). A learning algorithm is to select anappropriate estimation value of the parameter θ, using a learning samplefrom a hypothesis set {h(x,θ)}, which is called a learning model.

An algorithm called ensemble learning is aimed at selecting varioushypotheses in accordance with the difference in the weighting andinitial values of provided learning samples and combining these toconstruct a final hypothesis, by using a relatively simple learningmodel and a learning rule of a reasonable quantity of calculation. Thus,it is aimed at learning equivalent to learning with a complicatedlearning model.

In ensemble learning, since many hypotheses are combined to improveperformance, a learning algorithm used for ensemble learning is called aweak learning algorithm or weak learner, and a hypothesis is called aweak hypothesis, weak discriminator, weak judgment unit or the like.

Attempts to combine simple learners to produce a complicated one havelong been carried out in the field of neural networks. A learnerproduced in this manner or its algorithm is referred to as a combiningpredictor, combining learner, committee machine, modular network, votingnetwork, ensemble learning or the like. In this specification, a term“ensemble learning” is used.

When plural different parameters are given by learning as describedabove, a final output is decided by taking majority vote. If weighing wiis given to a hypothesis hi (normally, the sum of weighting isnormalized to be 1), this weighting indicates which hypothesis should beoutputted preferentially. Majority vote based on this weighting iscalled weighted vote. Majority vote in the case of equal weighting iscalled equal vote. If the output is meterage-like, the result ofweighting and adding the outputs of hypotheses is the final output.

A learner acquired by ensemble learning is also called a finalhypothesis or strong discriminator and it includes many weak hypothesesand a combiner for combining them. Depending on whether the operation ofthe combiner is dynamic or static with respect to an input and whetherthe way weak hypotheses are generated is parallel or sequential,classification into several learning algorithms is carried out. In thisembodiment, a face detection apparatus and a facial expressionrecognition apparatus will be described as static combiners thatintegrate outputs of weak hypotheses with fixed weighting irrespectiveof input, and as learners acquired by boosting for sequentiallygenerating hypotheses. As a similarly static combiner, there is boostingfor generating hypotheses in parallel.

In boosting, for example, several thousand detection targets andnon-detection targets, called learning samples, which have been labeledin advance, for example, samples including face images and non-faceimages are used, and different learners (weak hypotheses) are generatedwhile the weighting of the samples is sequentially changed. Then, theseare combined to construct a learner (final hypothesis) having highaccuracy. The term “boosting” is used because the accuracy of thelearning algorithm is boosted.

In this manner, from a learning model having a very simple structure andmade up of a combination of weak hypotheses, each of which has, initself, low discrimination performance to discriminate a detectiontarget or non-detection target, one hypothesis is selected in accordancewith a predetermined learning algorithm such as boosting, thusgenerating a weak hypothesis. As many weak hypotheses are combined, afinal hypothesis (discriminator) having high discrimination performancecan be acquired from the weak hypotheses, each of which has lowdiscrimination performance in itself. For example, in Adaboost,weighting is set for learning samples and data weighting is sequentiallyupdated so that large weighting is set for a sample that is difficult todiscriminate. For example, a weak hypothesis having the minimumdiscrimination error with respect to the weighted sample is selectedfrom many weak hypotheses, thus sequentially generating weak hypotheses.Also, reliability indicating the discrimination performance of thegenerated weak hypotheses is learned. In the following description,plural hypotheses (weak hypotheses) constituting a learning model willalso be referred to as filters when necessary, in order to discriminatethem from weak hypotheses sequentially generated by learning. Theresults of discrimination (results of output) of weak hypotheses willalso be referred to as estimation values or results of estimation whennecessary, in order to discriminate them from the results ofdiscrimination of a discriminator as a final hypothesis.

In this embodiment, a technique for realizing high-speed processing bygenerating weak hypotheses very efficiently in ensemble learning isproposed. Although depending on a discrimination target (detectiontarget) and its conditions, normally, there are a large number ofcombinations of weak hypotheses (filter) to be learning models. Inlearning, since processing to select one filter having the highestpossible discrimination performance from these many filters and togenerate a weak hypothesis is repeated, the processing itself usuallybecomes extremely large. On the other hand, with the weak hypothesisgeneration method according to this embodiment, a weak hypothesis havinghigh discrimination performance can be generated, even reducing thequantity of calculation at the time of generation.

Moreover, the final hypothesis acquired by learning includes many weakhypotheses. In discrimination, a weighted vote acquired by weightedaddition of all the outputs of these weak hypotheses is the output ofthe final hypothesis. Therefore, normally, the outputs of all the weakhypotheses must be acquired. On the other hand, in this embodiment, asan abort threshold value, which will be described later, is learned inlearning, whether data provided as an input is a detection target ornon-detection target can be sequentially judged, without taking aweighted vote among the outputs of all the weak hypotheses, and thearithmetic operation can be aborted without waiting for the results ofoutput of all the weak hypotheses. Therefore, the detection processingcan be performed at a higher speed. The method for generating weakhypotheses in this invention may be applied to ensemble learning otherthan boosting so as to similarly realize high-speed learning anddetection of a learner.

(1) Facial Expression Recognition System

FIG. 4 is a functional block diagram showing processing functions of afacial expression recognition system in this embodiment. As shown inFIG. 4, a facial expression recognition system 1 has a face detectionapparatus 10 that outputs the position and size of a face from aprovided input image, and a facial expression recognition apparatus 20that recognizes the expression of the face image detected by the facedetection apparatus.

The face detection apparatus 10 has an image output unit 11 to which adynamic image such as video image or a static image is inputted andwhich outputs a variable density image (brightness image), an integralimage generation unit 12 for generating an integral image, which will bedescribed later, from the variable density image outputted from theimage output unit 11, a scanning unit 13 for sequentially scanning theintegral image by using the size of a detection target, for example,from the upper left corner, and a discriminator 14 for discriminatingwhether each of all the window images sequentially scanned by thescanning unit 13 represents a face or not. The scanning unit 13sequentially scans each integral window by using a window with the sizeof a target object to be detected, and cuts out the window image. Thediscriminator 14 discriminates whether each window image represents aface or not. The position and size of an area representing the detectiontarget in the provided image (input image) are thus outputted.

The discriminator 14 discriminates whether the current window image is aface image or non-face image, referring to the result of learning by anensemble learner 15 that learns plural weak hypotheses constituting thediscriminator 14 by ensemble learning.

When plural face images are detected from an input image, this facedetection apparatus 10 outputs area information of plural areas. Ifthere are overlapping areas of the plural areas, processing to output anaverage area of these or to select an area having a value for takinghigh weighted vote, which will be described later, as an area evaluatedas having the highest probability of being a detection target, can becarried out.

The facial expression recognition apparatus 20 has a face featureextracting unit 21 for extracting a feature quantity for expressionrecognition from the face image detected by the face detection apparatus10, and an expression recognizing unit 22 for identifying the inputtedface image as one of plural facial expressions that have been learned inadvance, using the feature quantity extracted by the face featureextracting unit 21, thus recognizing the expression.

The face feature extracting unit 21 is formed by a Gabor filter forfiltering the face image using plural filters having directionselectivity and different frequency components. The expressionrecognizing unit 22 has expression identifiers corresponding to thetypes of expressions to be identified, to which the result of extractionof the face feature by the face feature extracting unit 21 is inputtedand which identify specific expressions, respectively. In thisembodiment, the expression recognizing unit 22 includes seven expressionidentifiers for identifying seven face images.

Data for the discriminator 14 of the face detection apparatus 10 hasbeen machine-learned by ensemble learning, using a learning data setincluding plural learning samples each of which has been labeled inadvance as a detection target or non-detection target. Data for thefacial expression recognition apparatus 20 has been learned, using imagesamples labeled with predetermined expressions in advance. Therefore,the facial expression recognition system will now be described in detailby the description of a learning method for the face detectionapparatus, a detection method by the face detection apparatus, alearning method for the facial expression recognition apparatus, and arecognition method by the facial expression recognition apparatus, inthis order.

The face detection apparatus 10 has a function of preprocessing such asgenerating an integral image and cutting out a predetermined area,before the discriminator 14. The discriminator 14 is adapted fordiscriminating whether an image provided as an input is a face image ornot. Therefore, when preprocessing is not necessary, the discriminator14 can be used as the face detection apparatus. Although thediscriminator 14 described in this embodiment is applied to the facedetection apparatus for discriminating a face image from a providedwindow image, it can also be applied to an apparatus for detecting adesired detection target other than a face.

(2) Discriminator

The discriminator 14 used in the face detection apparatus 10 in thisembodiment is adapted for taking a weighted vote among the results ofoutput of plural weak hypotheses so as to discriminate whether an inputimage is a detection target or not, that is, whether it is a face imageor not. The weak hypotheses and weighting on them have been learned inadvance by ensemble learning such as boosting.

The discriminator 14 as a learner acquired by ensemble learning hasplural weak hypotheses (weak hypothesis units) 14 b for extracting afeature quantity of an input image provided from an input unit 14 a andoutputting estimation values with respect to whether the input image isa detection target or not on the basis of the feature quantity, and acombiner 14 c for combining the estimation values, which are outputs ofthese weak hypotheses 14 b, as shown in FIG. 5. In the discriminator 14,an output unit 14 d discriminates whether the input image is a detectiontarget or not on the basis of the result of output from the combiner 14c. As described above, boosting requires the combiner 14 c forintegrating the outputs of the weak hypotheses by using fixed weightingirrespective of the input. In boosting, the distribution of learningsamples is processed in such a manner that the weighting on difficultlearning samples is increased using the result of learning of thepreviously generated weak hypotheses, and new weak hypotheses arelearned on the basis of this distribution. Therefore, the weighting onlearning samples that often become incorrect and therefore cannot bediscriminated as detection targets is relatively increased, and weakhypotheses that cause the learning samples with large weighting, thatis, the learning samples that are hard to discriminate, to be correct,are sequentially selected. That is, weak hypotheses are sequentiallygenerated in learning and weak hypotheses generated later depend onpreviously generated weak hypotheses.

In detection, the results of detection based on the many weak hypothesesthat are sequentially generated as described above and reliability(weighting) of discrimination performance of the weak hypotheses aremultiplied and added, and the result of this multiplication and additionis used as a result of discrimination. For example, in the case ofAdaboost, all the deterministic values outputted form weak hypothesesgenerated in this learning, that is, all the values of 1 for detectiontargets and −1 for non-detection targets, are supplied to the combiner14 c. The combiner 14 c performs weighted addition of the reliabilitycalculated for each of the corresponding weak hypotheses at the time oflearning, and the output unit 14 d outputs the result of a weighted votebased on the sum value. In accordance with whether this output ispositive or negative, it is possible to determine an input image is adetection target or not. While the weak hypotheses may deterministicallyoutput whether an input image is a detection target or not as inAdaboost, an algorithm such as Gentleboost or Real Adaboost, which willbe described later, can be used and weak hypotheses forprobabilistically outputting the probability of being a detection targetcan be used to further improve the discrimination performance.

(3) Learning Method for Face Detection Apparatus

Now, a learning method by the learner 15 for providing the discriminator14 as a final hypothesis formed by combining many appropriate weakhypotheses in accordance with a learning algorithm will be described. Inthe learning for the discriminator 14 for performing face detection,weak hypotheses for outputting estimation values indicating whetherprovided data is a face image or not are generated by using a learningdata set including plural learning samples each of which has beenlabeled as a face image representing a detection target or a non-faceimage representing a non-detection target such as a scenery image. Dataweighting is set for each learning sample, and when a weak hypothesis isgenerated, an error rate of the estimation value of the generated weakhypothesis with respect to the data set is calculated on the basis ofthe data weighting and the reliability of the weak hypothesis iscalculated on the basis of this error rate. Then, the data weighting oflearning samples on which the generated weak hypothesis made an error inestimation is updated so as to be relatively larger than the dataweighting of correctly estimated learning samples. After the dataweighting is thus updated, the processing to generate a weak hypothesisis repeated.

(3-1) Weak Hypothesis

As described above, in ensemble learning, one filter is selected from alearning model made up of a set of many filters, thereby generating aweak hypothesis. First, a filter to be used as a weak hypothesis usedfor face detection will be described. In this embodiment, as a learningmodel (set of weak hypotheses), filters (which will also be referred toas rectangle features) that output the difference between the sum ofbrightness values in one or plural rectangular boxes, of a rectangularbox group including two or more rectangular boxes, and the sum ofbrightness values in the other rectangular boxes, are used. In thisembodiment, weak hypotheses for outputting whether a provided image is adetection target or not are formed in accordance with the outputs ofthese filters. The filters are not limited to such rectangle features,and any filter can be used to form a weak hypothesis as long as it canform a weak hypothesis capable of discriminating whether an input imageis a face image or non-face image at a certain probability when a dataset is inputted.

FIG. 6 is a schematic view showing filters (rectangle features) used asweak hypotheses for face detection. To provide feature quantities forface detection, filters such as Haar basis functions are used. That is,plural filters are prepared, each of which outputs the differencebetween the sum of brightness values in one or plural rectangle boxesand the sum of brightness values in the other rectangle boxes of a groupof two or more rectangular boxes of the same size in each of inputimages 10A to 10D. For example, in the input image 10A, a filter 11A isprovided that subtracts the sum of brightness values in a shadedrectangular box 11A-2, of rectangular boxes 11A-1 and 11A-2 formed byhorizontally bisecting one rectangular box, from the sum of brightnessvalues in the rectangular box 11A-1. In the input image 10B, a filter11B is provided that subtracts the sum of brightness values in a shadedrectangular box 11B-2, of rectangular boxes 11B-1 and 11B-2 formed byvertically bisecting one rectangular box, from the sum of brightnessvalues in the rectangular box 11B-1. Such a filter including tworectangular boxes is called a two-rectangle feature. In the input image10C, a filter 11C is provided that subtracts the sum of brightnessvalues in a shaded central rectangular box 11C-2, of three rectangularboxes 11C-1 to 11C-3 formed by dividing one rectangular box into threeboxes, from the sum of brightness values in the rectangular boxes 11C-1and 11C-3. Such a filter including three rectangular boxes is called athree-rectangle feature. In the input image 10D, a filter 11D isprovided that subtracts the sum of brightness values in shadedrectangular boxes 11D-2 and 11D-4, of four rectangular boxes 11D-1 to11D-4 formed by vertically and horizontally dividing one rectangularbox, from the sum of brightness values in the rectangular boxes 11D-1and 11D-3 that are not adjacent to each other. Such a filter includingfour rectangular boxes is a called four-rectangle feature.

For example, a case of judging a face image 30 shown in FIG. 7 as a faceimage by using rectangle features as described above will be described.A two-rectangle feature 31A is a filter that subtracts the sum ofbrightness values in a shaded upper rectangular box 31A-2, of tworectangular boxes 31A-1 and 31A-2 formed by vertically bisecting onerectangular box, from the sum of brightness values in the lowerrectangular box 31A-2. Utilizing the fact that the brightness value islower in an eye area than in a cheek area of the human face image(detection target) 30, the rectangle feature 31A can be arranged over anarea including the eyes and nose to estimate whether the input image isa face image or not (correct or incorrect) at a certain probability froman output value of the rectangle feature 31A.

A three-rectangle feature 31B is a filter that subtracts the sum ofbrightness values in left and right rectangular boxes 31B-1 and 31B-3from the sum of brightness values in a central rectangular box 31B-2. Asin the above-described case, utilizing the fact that the brightnessvalue is higher in a nose area than in the areas of the eyes, therectangle feature 31B can be arranged at the positions of the eyes tojudge whether the input image is a face image or not to a certain extentfrom an output value of the rectangle feature 31B.

In this manner, there are various filters ranging from the filter thattakes the difference between two rectangular boxes to the filter thattakes the difference between four rectangular boxes such as therectangle feature 31C. Also a filter including rectangular boxes ofarbitrary position and arbitrary size (one or more pixels) can beselected. Even if the target area is limited to a 24×24-pixel area,there are 160,000 or more possible filters to be selected.

First, images called integral images are used to calculate outputs ofsuch filter at a high speed. An integral image is a image such that thevalue of a pixel P at (x, y) is the sum of brightness values of thepixels above and to the left of the pixel P in an image 40, as shown inFIG. 8A. That is, the value of the pixel P is the sum of brightnessvalues of the pixels contained in an upper left rectangular box 41 aboveand to the left of the pixel P. Hereinafter, an image such that eachpixel value is the value expressed by the following equation (1) iscalled an integral image.

$\begin{matrix}{{I\left( {x,y} \right)} = {\sum\limits_{{x^{\prime} < x},{y^{\prime} < y}}^{\;}{S\left( {x^{\prime},y^{\prime}} \right)}}} & (1)\end{matrix}$

As this integral image 40 is used, a rectangular box of an arbitrarysize can be calculated at a high speed. That is, as shown in FIG. 8B, anupper left rectangular box 41A, a rectangular box 41B on the right sideof the rectangular box 41A, a rectangular box 41C below the rectangularbox 41A, and a rectangular box 41D below and to the right of therectangular box 41A are provided, and the four vertexes of therectangular box 41D are referred to P1, P2, P3 and P4 clockwise from theupper left vertex. In this case, the value at P1 is the sum A ofbrightness values in the rectangular box 41A (i.e., P1=A). The value atP2 is the sum B of A and brightness values in the rectangular box 41B(i.e., P2=A+B). The value at P3 is the sum B of A and brightness valuesin the rectangular box 41C (i.e., P3=A+C). The value at P4 is the sum Dof A+B+C and brightness values in the rectangular box 41D (i.e.,P4=A+B+C+D). The sum of brightness values in the rectangular box 41D canbe calculated as P4−(P2+P3)−P1. By adding or subtracting the pixelvalues at the four corners of the rectangular box, it is possible tocalculate the sum of brightness values in the rectangular box at a highspeed.

As one of such filters is selected and the value in the case where aprovided image is a face image is learned as a feature quantity from anoutput value acquired by filtering a learning data set, a weakhypothesis can be generated. A weak hypothesis in Adaboost, at the timeof discrimination, compares the learned feature quantity with a valueacquired by filtering a provided input image so as to output a binaryvalue representing whether the provided input image is a face image (=1)or non-face image (=−1).

Alternatively, as outputs of weak hypotheses, by employing a boostingalgorithm for selecting filters that realize minimum weighted squaredifference between output values (real values) of the filters and labelvalues (1, −1) of samples, and their feature quantities, and adding thereal values, instead of a weak hypothesis that deterministically outputsa binary value representing whether an input image is a face image ornot as in Adaboost, it is possible to carry out more efficient learning.Such a boosting algorithm is called Gentleboost, which is described in,for example, J. Friedman, T, Hastie, and R. Tibshirani, “Additivelogistic regression: A statistical view of boosting,” ANNALS OFSTATISTICS, 28(2): 337-374, 2000. There is another boosting algorithmcalled Real Adaboost for making probabilistic outputs as outputs of weakhypotheses, like Gentleboost.

Now, learning methods for the face detection apparatus using each of thealgorithms Adaboost, Real Adaboost, and Gentleboost will be described.Prior to the explanation of these learning methods, an abort thresholdvalue, which is characteristic data of data learned by the learner 15 inthis embodiment, will be described first. An abort threshold value is athreshold value for aborting detection during the discrimination process(detection process), and is learned data that is not learned in normalboosting learning.

(3-2) Abort Threshold Value

In ensemble learning, normally, data provided by taking a weighted voteamong outputs of all the weak hypotheses constituting the discriminator14 is learned for the discriminator to discriminate whether an input isa detection target or not, as described above. The weighted vote isoutputted as the result of comparison between a value (hereinafterreferred to as sum value) acquired by adding the products of the resultof discrimination (estimation value) of weak hypotheses and theirreliability, and a discrimination boundary value. For example, when thenumber of weak hypotheses is t (=1, . . . , K), the weighting on amajority vote corresponding to each weak hypothesis (reliability) is at,and the output of each weak hypothesis is ht, the value (sum value) fortaking a weighted vote in Adaboost can be calculated by the followingequation (2). In this equation, x represents a learning sample. In thiscase, it is made up of the vectors of pixel values.

$\begin{matrix}{{Sum}\mspace{14mu}{value}\text{:}{\sum\limits_{t}^{\;}{\alpha_{t}{h_{t}(x)}}}} & (2)\end{matrix}$

FIG. 9 is a graph showing changes corresponding to whether an inputtedimage is a detection target or not, with the horizontal axisrepresenting the number of weak hypotheses and the vertical axisrepresenting the value (sum value) for taking weighted vote expressed bythe equation (2). In FIG. 9, for data D1 to D4 indicated by solid lines,estimation values ht(x) are sequentially calculated by weak hypothesesfrom images (learning samples) labeled as faces and are added. As thesedata D1 to D4 show, a value acquired by multiplying the estimationvalues ht(x) calculated by a certain number of weak hypotheses that takeface images as input images by the reliability and then adding them, ispositive. In Adaboost, this sum value is judged by using adiscrimination boundary value 0, and if the sum value is positive, aresult showing that an input is a detection target is outputted.

In this embodiment, a technique different from the normal boostingalgorithm is used. Specifically, in the process of sequentially addingthe results of discrimination by the weak hypotheses, if it can bediscriminated that an input is obviously not a detection target, thatis, not a face, discrimination of that window image is stopped evenbefore the results of output of all the weak hypotheses are acquired. Inthis case, a value for deciding whether or not to stop thediscrimination is learned in the learning process. Hereinafter, thevalue used for deciding whether or not to stop the discrimination iscalled the abort threshold value.

With this abort threshold value, when a non-face can be certainlyestimated with respect to all the window images, the calculation of theestimation value ht(x) of the weak hypothesis can be stopped even if theresults of output of all the weak hypotheses are not used. Therefore,the quantity of arithmetic operation can be significantly reduced,compared with the case of taking weighted vote using all the weakhypotheses.

As this abort threshold value, the smaller value of a minimum value thatcan be taken by the value of a weighted vote among the results ofdiscrimination of learning samples (positive data) labeled as face, ofthe learning samples, and the discrimination boundary value, can beused. In the discrimination process, the outputs (estimation valuesht(x)) from the weak hypotheses with respect to the window images aresequentially weighted and added, and the result is outputted. That is,this sum value is sequentially updated, and this updated value iscompared with the abort threshold value every time an update is made,that is, every time one weak hypothesis outputs the estimation value. Ifthe updated sum value is less than the abort threshold value, it can bedecided that the window image is not a face image and the calculation ofthe weak hypothesis can be aborted. Therefore, redundant calculation canbe omitted and the discrimination processing can be performed at ahigher speed.

Specifically, an abort threshold value RK of an output hK(xi) of theK-th weak hypothesis is the smaller value of a minimum weighted votevalue in the case where a learning sample (also referred to as positivesample or positive data) xj (=x1 to xJ), which is a face image, oflearning samples xi (=x1 to xN), and the discrimination boundary value.It can be expressed by the following equation (3)

$\begin{matrix}{{{Abort}\mspace{14mu}{threshold}\mspace{14mu}{value}\text{:}}{R_{K} = {\min\left( {{\sum\limits_{t = 1}^{K}\;{\alpha_{t}{h_{t}\left( x_{1} \right)}}},{\sum\limits_{t = 1}^{K}\;{\alpha_{t}{h_{t}\left( x_{2} \right)}}},...\mspace{14mu},{\sum\limits_{t = 1}^{K}\;{\alpha_{t}{h_{t}\left( x_{J} \right)}}}, 0} \right)}}} & (3)\end{matrix}$

As shown in this equation (3), when the minimum value for taking aweighted vote of the learning samples x1 to xJ as detection targets ismore than 0, 0 is set as the abort threshold value RK. 0 is not exceededin the case of Adaboost for carrying out discrimination using adiscrimination boundary value of 0. It depends on the technique ofensemble learning. In the case of Adaboost, the abort threshold value isset at the minimum possible values of the data D1 to D4 in the casewhere a face image as a detection target is inputted as an input image,as indicated by a bold line in FIG. 9. When the minimum values of allthe data D1 to D4 exceed 0, the abort threshold value is set at 0.

In this embodiment, as the abort threshold value Rt (R1 to RT where thenumber of weak hypotheses to be generated is T) is learned every time aweak hypothesis is generated, estimation values are sequentiallyoutputted by the plural weak hypotheses and a value acquired by addingthese values is sequentially updated in the discrimination process,which will be described later. For example, as in the case of data D5,the discrimination processing by the subsequent weak hypothesis can beended when the value acquired by sequentially adding values becomeslower than the abort threshold value. That is, by learning this abortthreshold value Rt in advance, it is possible to decide whether or notto calculate the next weak hypothesis every time the estimation value ofa weak hypothesis is calculated. When an input is obviously not adetection target, it can be judged that an input is a non-detectiontarget without waiting for the results of discrimination of all the weakhypotheses. As the arithmetic operation is thus aborted, high-speeddetection processing can be realized.

In the following description, the abort threshold value for aborting theprocessing on the basis of a judgment that a provided image is obviouslynot a detection target at the time of detection will be described.However, an abort threshold value for aborting the processing on thebasis of a judgment that a provided image is obviously a detectiontarget may be learned similarly. In this case, a larger value of amaximum possible value of weighted vote value among the results ofdiscrimination of learning samples (also referred to as negative samplesor negative data) labeled as non-face image, of learning samples, and adiscrimination boundary value, can be used as the abort threshold value.In the detection processing, a sum value acquired by sequentially addingproducts of outputs of weak hypotheses and their reliability is comparedwith the abort threshold value, and when the sum value is larger thanthe abort threshold value, it is possible to judge that the image thatis now being judged is obviously a face image and to end thediscrimination processing.

(3-3) Structure of Learner

First, the structure of the learner 15 will be described. FIG. 10 is afunctional block diagram showing the learner 15. As shown in FIG. 10,the learner 15 has a database 31 in which a learning data set is stored,a selecting unit 33 for selecting a desired number of weak hypothesesfrom a learning model 32 made up of a set of many filters, a new weakhypothesis generating unit 34 for generating a new weak hypothesis byusing weak hypotheses outputted from the selecting unit 33, and a weakhypothesis selecting unit 35 for selecting one weak hypothesis havingthe highest discrimination performance from the weak hypotheses selectedby the selecting unit 33 and the new hypothesis generated by the newweak hypothesis generating unit 34. These units constitute a weakhypothesis generation apparatus. The learner 15 also has a reliabilitycalculating unit 36 for calculating reliability representing thediscrimination performance of the weak hypothesis generated by theselection by the weak hypothesis selecting unit 35, an abort thresholdvalue calculating unit 37 as an abort threshold value learning unit forcalculating an abort threshold value to decide whether or not to abortestimation value calculation processing when the discriminator 14performs discrimination, and a data weighting updating unit 38 forupdating data weighting on each learning sample in the learning data seton the basis of the result of reliability calculation. When the dataweighting on each learning sample included in the learning data set 31is updated by the data weighting updating unit 38, the weak hypothesisgeneration apparatus executes the processing to generate a next weakhypothesis. The repetitive processing to update the data weighting onthe learning data set and generate a weak hypothesis by the weakhypothesis generation apparatus is repeated until a final hypothesishaving discrimination capability that is required by the system isacquired.

The learning data set stored in the database 31 includes a group ofimages formed by cutting out areas representing detection targets (inthis embodiment, a face image group), and a group of random imagesformed by cutting out images of non-detection targets such as sceneryimages.

The selecting unit 33 can select weak hypotheses from the learning modelat a predetermined rate, for example, approximately 5%, and output theseselected weak hypotheses to the new weak hypothesis generating unit 34and the weak hypothesis selecting unit 35. However, if the selectingunit 33 selects one or plural weak hypotheses having high discriminationperformance as high-performance weak hypotheses from these hypothesesand outputs them to the new weak hypothesis generating unit 34 and theweak hypothesis selecting unit 35, a weak hypothesis having higherdiscrimination performance can be generated. The weak hypothesisselecting unit 35 first selects one filter from the learning model andlearns the feature quantity of the filter by using the learning dataset. That is, as a feature quantity that minimizes the discriminationerror when the learning data set is discriminated is learned, a weakhypothesis is generated. In the case where weak hypotheses output binaryvalues as the results of estimation, the feature quantity to be learnedis a discrimination threshold. This processing is repeated for thenumber of times corresponding to the number of selected filters so as togenerate weak hypotheses, and one or more weak hypotheses having a lowererror rate are selected from the generated weak hypotheses, ashigh-performance weak hypotheses.

The new weak hypothesis generating unit 34 adds a predeterminedmodification to the filters (high-performance filters) employed for theweak hypotheses outputted from the selecting unit 33, for example,high-performance weak hypotheses, and thus generates one or moresubtypes of the high-performance filters. The new weak hypothesisgenerating unit 34 then learns their feature quantities by using thelearning data set so as to generate a new weak hypothesis, and outputsit to the weak hypothesis selecting unit 35.

The abort threshold value calculating unit 37, if the present repetitionis the t-th time, multiplies the reliability calculated by thereliability calculating unit 36, by the result of estimation of positivedata included in the learning data set by the weak hypothesis selectedby the weak hypothesis selecting unit 35, then adds the result ofmultiplication to the abort threshold value learned in the previousrepetitive processing ((t−1)th repetition), and takes the resultingvalue as an abort threshold value in the t-th repetition.

The data weighting updating unit 38 processes distribution followed bythe learning samples in such a manner that the weighting on difficultlearning samples is increased using the result of learning of thepreviously generated weak hypotheses, as described above. Therefore, theweighting on learning samples that often become incorrect and thereforecannot be discriminated as detection targets is relatively increased.

As new weak hypotheses are learned in this manner on the basis of thedistribution of the updated data weighting until a final hypothesis isacquired by boosting, weak hypotheses that cause the learning sampleswith large weighting, that is, the learning samples that are hard todiscriminate, to be correct, are sequentially generated.

In the learner 15, the weak hypothesis generated by the weak hypothesisselecting unit 35 is outputted as the result of the t-th repetitivelearning, and its reliability is calculated by the reliabilitycalculating unit 36. The abort threshold value is outputted from theabort threshold value calculating unit 37. These data are saved and usedby the discriminator 14 at the time of discrimination. Specifically, inthe case of using the above-described rectangle features for filters,the data outputted from the weak hypothesis selecting unit 35 are thepositions and sizes of the group of rectangular boxes constituting therectangle features, and the feature quantities acquired whensubtracting, from the sum of brightness values in one or pluralrectangular boxes, the sum of brightness values in the other rectangularboxes.

(3-4) Adaboost Algorithm

Now, the learning methods for the discriminator 14 by theabove-described learner 15 will be described. First, a learning methodaccording to the Adaboost algorithm will be described. Theabove-described learning data set including plural training data thathave been manually labeled in advance is prepared as a premise of apattern recognition problem based on typical two-class discriminationsuch as a problem of discriminating whether provided data is a face ornot.

The learning algorithm is applied on the basis of the learning data set,thus generating learned data to be used for discrimination. In thisembodiment, the learned data to be used for discrimination are thefollowing four types of learned data including the above-described abortthreshold value:

(A) weak hypotheses (T units);

(B) threshold values of weak hypotheses (T units);

(C) weighting of weighted vote (reliability of weak hypotheses) (Tunits); and

(D) abort threshold values (T units).

(3-4-1) Learning for Discriminator 14

Hereinafter, algorithms for learning the above-described four types oflearned data (A) to (D) from many learning samples as described abovewill be described. FIG. 11 is a flowchart showing a method for learningdata for the discriminator.

Procedure 0: Labeling of Learning Samples

As described above, i=N learning samples (xi, yi) are prepared, each ofwhich has been labeled in advance as a detection target or non-detectiontarget.

In the learning samples (xi, yi): (x1, y1), . . . , (xN, yN), xiεX andyiε{−1, 1} hold. X represents the data of a learning sample. Yrepresents the label (correct) of a learning sample. N represents thenumber of learning samples. That is, xi represents a feature vectorconstituted by all the brightness values in a learning sample image.yi=−1 represents a case where a learning sample has been labeled as anon-detection target. yi=1 represents a case where a learning sample hasbeen labeled as a detection target.

Procedure 1) Initialization of Data Weighting

In boosting, weighting (data weighting) on the individual learningsamples are varied and the data weighting on a learning sample that isdifficult to discriminate is relatively increased. The result ofdiscrimination is used for calculating an error rate for evaluating weakhypotheses. As the result of discrimination is multiplied by the dataweighting, a weak hypothesis that makes an error in discriminating amore difficult learning sample is evaluated as having a discriminationrate lower than the actual discrimination rate. The data weighting issequentially updated in this manner. First, the data weighting on thelearning samples is initialized. The initialization of the dataweighting on the learning samples is carried out as the data weightingupdating unit 38 makes even distribution of the weighting on all thelearning samples. It is defined by the following equation (4) (step S1).

$\begin{matrix}{{{Initialization}\mspace{14mu}{of}\mspace{14mu}{data}\mspace{14mu}{weighting}\text{:}\mspace{14mu}{D_{1}(i)}} = \frac{1}{N}} & (4)\end{matrix}$

In this equation, data weighting D1(i) on the learning samplesrepresents data weighting on learning samples xi (=xi to xN) of thefirst repetition (the number of repetitions t=1), and N represents thenumber of samples.

Procedure 2) Repetitive Processing

Next, as the following processing of steps S2 to S6 is repeated, weakhypotheses are sequentially generated and data for the discriminator arelearned. The number of repetitions is expressed by t=1, 2, . . . , T.Every time the repetitive processing is carried out once, one weakhypothesis, that is, one filter, and a feature quantity fordiscriminating data provided as an input on the basis of its filteroutput, are learned. Therefore, weak hypotheses corresponding to thenumber of repetitions (T) are generated, and a discriminator made up ofT weak hypotheses is generated. As the repetitive processing is carriedout several hundred to several thousand times, several hundred toseveral thousand weak hypotheses are generated. The number ofrepetitions (i.e., number of weak hypotheses) t may be suitably set inaccordance with the required discrimination performance and the problem(detection target) to be discriminated.

First, weak hypotheses are generated by the weak hypothesis generationapparatus (step S2). In this case, a filter that minimizes a weightederror rate εt expressed by the following equation (5) is learned fromfilters selected and generated by a method that will be described later.

$\begin{matrix}{{{Weighted}\mspace{14mu}{error}\mspace{14mu}{rate}\text{:}\mspace{14mu} ɛ_{t}} = {\underset{i:{{h_{t}{(x_{i})}} \neq y_{i}}}{\overset{\;}{\sum D_{t}}}(i)}} & (5)\end{matrix}$

As shown in the equation (5), the weighted error rate εt is the sum ofonly the data weighting Dt on learning samples such that the result ofdiscrimination by the weak hypothesis is an error (ht(xi)≠yi), of thelearning samples. If an error is made in the discrimination of alearning sample having larger data weighting (more difficult todiscriminate), the weighted error rate εt is increased.

Then, the reliability calculating unit 36 calculates weighting at fortaking a weighted vote in accordance with the following equation (6) onthe basis of the weighted error rate εt expressed by the equation (5) ofthe weak hypotheses generated by learning (step S3). The weighting atfor a weighted vote indicates discrimination performance of a weakhypothesis learned in the t-th repetitive processing. Hereinafter, theweighting set for each weak hypothesis for calculating weighted vote iscalled reliability.

$\begin{matrix}{{{Reliability}\text{:}\mspace{14mu}\alpha_{t}} = {\frac{1}{2}{\ln\left( \frac{1 - ɛ_{t}}{ɛ_{t}} \right)}}} & (6)\end{matrix}$

As expressed by the equation (6), the lower the weighted error rate εtis, the higher the reliability αt of the weak hypothesis is.

Next, unlike learning based on ordinary Adaboost, the abort thresholdvalue calculating unit 37 calculates an abort threshold value Rt foraborting discrimination in the discrimination process (step S4). As theabort threshold value Rt, the smaller value of a sum value of learningsamples as detection targets (positive learning samples) x1 to xJ and adiscrimination boundary value 0 is selected. As described above, in thecase of Adaboost where discrimination is carried out using 0 as adiscrimination boundary value, a minimum value or 0 is set as the abortthreshold value. The abort threshold value Rt is set to be a maximumvalue that at least all the positive learning samples can pass.

Then, using the reliability αt acquired by the equation (6), the dataweighting updating unit 38 updates the data weighting Dt(i) on thelearning samples, using the following equation (7). Zt is fornormalizing the data weighting.

$\begin{matrix}{{{Data}\mspace{14mu}{weighting}\text{:}\mspace{14mu}{D_{t + 1}(i)}} = \frac{{D_{t}(i)}{\exp\left( {{- \alpha_{i}}y_{i}{h_{t}\left( x_{i} \right)}} \right)}}{Z_{t}}} & (7)\end{matrix}$where Zt is a normalization factor to achieve

$\begin{matrix}{{\sum\limits_{i = 1}^{N}\;{D_{t + 1}(i)}} = 1} \\{Z_{t} = {\sum\limits_{i = 1}^{N}\;{{D_{t}(i)}{\exp\left( {{- \alpha_{i}}y_{i}{h_{t}\left( x_{i} \right)}} \right)}}}}\end{matrix}$

At step S7, whether or not boosting has been carried out a predeterminednumber of times (=T times) is judged. If not, the processing of steps S2to S7 is repeated. If learning has been done the predetermined number oftimes, the learning processing ends. For example, using a finalhypothesis at that point, made up of all the generated weak hypotheses,the processing may be repeated until the learning data set can bediscriminated with desired performance. It is also possible to preparean evaluation data set, which is different from the learning data setused for generating weak. hypotheses, and to evaluate the discriminationperformance of the final hypothesis by using the evaluation data set. Itis also possible to evaluate the final hypothesis by cross validation ofcarrying out learning with the learning data set from which one sampleis excluded and then repeating processing of evaluation with theexcluded one sample for the number of samples, or dividing the learningdata set into a predetermined number of groups, then carrying outlearning with the learning samples from which one group is excluded, andrepeating processing of evaluation with the excluded one group for thenumber of groups.

Procedure 3) Generation of Final Hypothesis (Discriminator)

A final hypothesis, which is to be the discriminator 14, is acquired bytaking a weighted vote among all the hypotheses using their reliability.That is, the outputs of the weak hypotheses generated at step S2 aremultiplied by the reliability calculated at step S4, and thediscriminator 14 for judging the sign of the value (sum value) fortaking the weighted vote expressed by the equation (2), in accordancewith the following equation (8), is generated. The discriminator 14 thusacquired outputs whether an input is a face or non-face, using adiscrimination function H expressed by the following equation (8). Ifthe discrimination function H is positive, the input is a face. If itis, negative, the input is a non-face.

$\begin{matrix}{{H(x)} = {{sgn}\left( {\sum\limits_{t = 1}^{T}\;{\alpha_{t}{h_{t}(x)}}} \right)}} & (8)\end{matrix}$(3-4-2) Generation of Weak Hypotheses

Next, the method for generating a weak hypothesis at the above-describedstep S2 (learning method) will be described. FIG. 12 is a flowchartshowing a weak hypothesis generation method. In the generation of a weakhypothesis in this embodiment, first, a part of plural weak hypothesesis selected, and from this selected part, a weak hypothesis having theminimum error rate or plural weak hypotheses having low error rates inestimating or discriminating the data set (hereinafter referred to ashigh-performance weak hypotheses) are selected. Then, one or more newweak hypotheses formed by adding a predetermined modification to thehigh-performance weak hypotheses are generated. From thehigh-performance weak hypotheses and the new weak hypotheses, a weakhypothesis having the minimum error rate in the data set estimationvalue is selected as a weak hypothesis. This enables high-speedgeneration of a weak hypothesis. This method for generating a weakhypothesis will now be described in detail.

As described above, even when a target area (window image) is limited toa 24×24-pixel area, there are 160,000 or more possible filters to beselected, depending on the number of pixels constituting the filter(size of filter) and the type of the filter such as two-, three- orfour-rectangle feature. As a method for selecting one of these 160,000filters, for example, it is possible to learn the feature quantities ofall the filters and select a filter having the highest discriminationperformance. However, a very large quantity of calculation is requiredand it is very time-consuming even when the above-described integralimages are used. Thus, in this embodiment, first, a predeterminedcomputable number of filters, for example, approximately 5%, of all thefilters are randomly selected by the selecting unit 33 shown in FIG. 10,and approximately 5% of all the weak hypotheses that can be generatedare generated. For this, the following processing of steps S11 to S14 isrepeated a predetermined number of times (hereinafter, M times), thusgenerating the predetermined number of weak hypotheses.

First, an arbitrary filter is selected from all the possible filters asdescribed above (step S11).

Next, output values by the filter selected at step S11 with respect toall the learning samples are calculated, and their histogram (frequencydistribution) is found (step S12).

Since a weak hypothesis based on Adaboost is to perform weakdiscrimination with a feature quantity bisected by a threshold value, athreshold value that minimizes the weighted error rate εt expressed bythe equation (5) is searched for. That is, a threshold value Thmin thatminimizes the weighted error rate εt (εmin) is calculated from thefrequency distribution found at step S12 (step S13).

As the threshold value Thmin, in a histogram with the horizontal axisrepresenting the filter output and the vertical axis representing thefrequency, a search value may be shifted in the direction of thehorizontal axis representing the filter output so as to find a valuethat minimizes the weighted error rate εt expressed by the equation (5).The weighted error rate εt is the smaller one of the correct answer rateand the incorrect answer rate of all the answers. In the case where thesearch value is changed, the sum of weighted count values of positivesamples for which answers are correct, and the sum of weighted countvalues of negative samples for which answers are correct, increase ordecrease by the amount of shifted search value. Therefore, it is notnecessary to re-calculate the sum of weighted count values of all thepositive samples and the sum of weighted count values of all thenegative samples with respect to each search value, and high-speedcalculation can be realized.

Then, whether the processing has been repeated the predetermined numberof times (=M times) or not is judged (step S14). The processing fromstep S11 is repeated until the predetermined number of times is reached.

Conventionally, it is necessary to select a filter having the minimumweighted error rate εt, acquired from the data weighting Dt(i) on thelearning samples at that point, for example, by repeating the processingof steps S11 to S14 for all the types of filters. In this embodiment,however, the repetitive processing of steps S11 to S14 is carried out,for example, for approximately 5% of all the selectable filters, asdescribed above. To generate weak hypotheses having high performancewithout trying all the filters, the new weak hypothesis generating unit34 executes the following processing of steps S15 to S17.

First, at step S15, one or plural weak hypotheses having a lowerweighted error rate εt, that is, weak hypotheses having highdiscrimination performance with respect to the data set, are selectedfrom the M weak hypotheses generated by the repetitive processing ofsteps S11 to S14 repeated M times. The selected weak hypotheses arehereinafter called high-performance weak hypotheses.

Next, a predetermined modification is added to the filters having thelower error rate used for high-performance weak hypotheses (hereinafterreferred to as high-performance filters), thus generating a new filteror new filters (step S16). This new filter can be generated inaccordance with a statistical characteristics or a genetic algorithm ofthe detection target. Specifically, the position of a high-performancefilter is shifted, for example, by approximately two pixels in thevertical direction and/or the horizontal direction, thus generating anew filter. Alternatively, the scale of a high-performance filter isenlarged or contracted by approximately two pixels in the verticaldirection and/or the horizontal direction, thus generating a new filter.Also, a high-performance filter is inverted with respect to a verticalline passing through a center point in the horizontal direction of animage, thus generating a new filter, or a composite filter made up ofthe high-performance filter and the inverted filter is used as a newfilter. These methods are suitably combined to generate one or more newfilters for each high-performance filter.

FIG. 13 is a schematic view showing inverted filters utilizing symmetry,as new filters. Rectangle features 21A to 21D shown in FIG. 13 areformed by inverting the rectangle features 11A to 11D shown in FIG. 6with respect to a vertical bisector 22 passing through the center in thehorizontal direction (x-direction) of an image. That is, the rectanglefeatures 11A to 11D and the rectangle features 21A to 21D are linearlysymmetrical with respect to the vertical bisector 22. This utilizes thefact that since a human face is almost symmetrical on the left and rightsides, there is a high possibility that a new filter generated byinverting a filter selected as having high face detection performanceshould be a filter having high performance. As the new filters are thusgenerated on the basis of the statistical characteristics of a face as adetection target or in accordance with the genetic algorithm from thehigh-performance filters selected as having high-performance from thepart of all the filter that has been tried for performance, thegenerated filter can be estimated to have high discriminationperformance similar to that of the selected high-performance filters. InFIG. 13, for example, in the case where the high-performance filter isthe rectangle feature 11A and the inverted filter is the rectanglefeature 21A, two types of new filters can be generated, that is, theinverted rectangle feature 21A, and a filter made up of the rectanglefeature 11A and the inverted feature 21A.

Then, the weak hypothesis selecting unit 35 shown in FIG. 10 selects onefilter that minimizes the weighted error rate εt, from the mixture ofthe high-performance filters and the generated new filters, and employsthe selected one filter as a weak hypothesis (step S17). As the filterhaving the highest discrimination performance is selected from themixture of the new filters and the original high-performance filters andis employed as a weak hypothesis, the filter having high discriminationperformance as in the case of searching for such a filter from all thefilters can be selected without searching for the filter having thehighest discrimination performance from all the filters, and theprocessing speed in filter selection can be significantly improved.

(3-5) Real Adaboost Algorithm

Now, the Real Adaboost algorithm will be described. Also in RealAdaboost, the same procedures 0 and 1 as in Adaboost are carried out. Alearning data set is prepared and data weighting on each learning sampleis first initialized (i.e., evenly distributed) in accordance with theequation (4).

Procedure 2) Repetitive Processing

Next, the following processing is repeated to sequentially generate weakhypotheses, and data for the discriminator 14 is learned. Similar toAdaboost, the number of repetitions is t=1, 2, . . . , T.

First, a weak hypothesis is generated by the weak hypothesis generationapparatus. This generation method is basically similar to theabove-described generation method in Adaboost. However, since a weakhypothesis is generated so as to output probability density based ondata weighting Dt (data weighting distribution), the probability densityPm(x) of feature quantity expressed by the following equation (9) iscalculated. The probability Pm(x) represents the correct answer ratewith respect to samples (y=1) labeled as faces of all the learningsamples, with the data weighting Dt.p _(m)(x)={circumflex over (P)}_(D)(y=1|x)ε[0,1]  (9)

Then, the reliability calculating unit 36 calculates the quantity ofcontribution fin of a weak hypothesis expressed by the followingequation (10) instead of the above-described reliability α.

$\begin{matrix}{\left. {{Quantity}\mspace{14mu}{of}\mspace{14mu}{contribution}\text{:}\mspace{14mu}{f_{m}(x)}}\leftarrow{\frac{1}{2}\log\frac{p_{m}(x)}{1 - {p_{m}(x)}}} \right. \in R} & (10)\end{matrix}$

R represents a set of real-number values.

This algorithm is different from Adaboost in that the weak hypothesisoutputs the quantity of contribution fm indicating the probabilitydensity, instead of the deterministic binary output. However, in thegeneration of the weak hypothesis, the selecting unit 33 selects one orseveral filters having a large quantity of contribution fm of weakhypothesis expressed by the equation (10) from a part of filters on thebasis of the data distribution Dt, the new weak hypothesis generatingunit 34 then generates a new filter in accordance with statisticalcharacteristics or genetic algorithm of a detection target (in thisembodiment, a human face), and the weak hypothesis selecting unit 35selects a filter having the highest discrimination performance fromthem. This is similar to the above-described technique. Therefore, theweak hypothesis generation processing can be carried out at a higherspeed without lowering the discrimination performance.

Next, the abort threshold value calculating unit 37 calculates an abortthreshold value Rt for aborting discrimination in the discriminationprocess, as described above. As the abort threshold value Rt, thesmaller value of the sum fm of quantities of contribution with respectto learning samples that are detection targets (positive learningsamples) x1 to xJ, instead of filter outputs h in Adaboost, and adiscrimination boundary value 0, may be selected. That is, the abortthreshold value Rt is set to be a maximum value that at least all thepositive learning samples can pass.

Next, the data weighting updating unit 38 updates the data weightingDt(i) on each learning sample i in the t-th repetitive processing inaccordance with the following equation (11) using the quantity ofcontribution fin.

$\begin{matrix}{\left. {{Data}\mspace{14mu}{weighting}\text{:}\mspace{14mu}{D_{t + 1}(i)}}\leftarrow{{D_{t}(i)}{\exp\left\lbrack {{- y_{i}}{f_{m}\left( x_{i} \right)}} \right\rbrack}} \right.\left. {D_{t}(i)}\leftarrow\frac{D_{t}(i)}{\Sigma_{i}{D_{t}(i)}} \right.} & (11)\end{matrix}$

Then, the processing is repeated a predetermined number of times (=Ttimes), and the T weak hypotheses, their quantities of contribution finand the abort threshold value are learned. As described above, thegeneration of weak hypotheses can be repeated until a final hypothesisformed by a combination of all the generated weak hypotheses candiscriminate the learning data set with desired performance. Thediscriminator, which provides the final hypothesis, can discriminatewhether an input is a face or non-face by judging whether the sign ofthe sum of quantities of contribution fm of all the hypotheses, that is,the discrimination function H expressed by the following equation (12),is positive or negative.

$\begin{matrix}{{H(x)} = {{sgn}\left( {\sum\limits_{t = 1}^{T}\;{f_{m}(x)}} \right)}} & (12)\end{matrix}$(3-6) Gentleboost Algorithm

Now, the Gentleboost algorithm will be described. Also in Gentleboost,the same procedures 0 and 1 as in Adaboost and Real Adaboost are carriedout. A data set including plural labeled learning samples is preparedand data weighting on each learning sample is initialized (i.e., evenlydistributed) in accordance with the equation (4).

Next, basically, the processing similar to the processing in RealAdaboost is repeated to sequentially generate weak hypotheses, and datafor the discriminator is learned. However, the outputs of the weakhypotheses are different from those in Real Adaboost. In this case,similar to Adaboost and Real Adaboost, the number of repetitions is t=1,2, . . . , T.

First, a weak hypothesis is generated by the weak hypothesis generationapparatus. The weak hypothesis selects a filter on the basis of dataweighting Dt (distribution of data weighting) and calculates a realfunction fin that minimizes a weighted square error εt expressed by thefollowing equation (13), using the feature quantity of the filter.

$\begin{matrix}{e_{t} = {\sum\limits_{i}^{N}\;{{D_{t}(i)}\left\lbrack {y_{i} - {f_{m}(x)}} \right\rbrack}^{2}}} & (13)\end{matrix}$

Also in Gentleboost, like Real Adaboost, in the generation of the weakhypothesis, the selecting unit 33 selects one or several filters havinga large sum of real functions fm(xi) of weak hypothesis from a part offilters on the basis of the data distribution Dt, the new weakhypothesis generating unit 34 then generates a filter in accordance withstatistical characteristics or genetic algorithm of a human face, andthe weak hypothesis selecting unit 35 selects a filter having thelargest sum of real functions from them. Therefore, the processing canbe carried out similarly at a higher speed.

Next, the abort threshold value calculating unit 37 calculates an abortthreshold value Rt for aborting discrimination in the discriminationprocess, as described above. As the abort threshold value Rt, thesmaller value of the sum fin of real functions with respect to learningsamples that are detection targets (positive learning samples) x1 to xJ,instead of filter outputs f(x) in Adaboost, and a discriminationboundary value 0, may be selected. That is, the abort threshold value Rtis set to be a maximum value that at least all the positive learningsamples can pass.

Next, the data weighting updating unit 38 updates the data weightingDt(i) on each learning sample i in the t-th repetitive processing inaccordance with the following equation (14), as in Real Adaboost, usingthe real functions fin.

$\begin{matrix}{\left. {{Data}\mspace{14mu}{weighting}\text{:}\mspace{25mu}{D_{t + 1}(i)}}\leftarrow{{D_{t}(i)}{\exp\left\lbrack {{- y_{i}}{f_{m}\left( x_{i} \right)}} \right\rbrack}} \right.\left. {D_{t}(i)}\leftarrow\frac{D_{t}(i)}{\Sigma_{i}{D_{t}(i)}} \right.} & (14)\end{matrix}$

Then, the processing is repeated a predetermined number of times (=Ttimes), and the T weak hypotheses, their real functions fm and the abortthreshold value are learned. The discriminator, which provides the finalhypothesis, can discriminate whether an input is a face or non-face byjudging whether the sign of the sum of real functions fin of all thehypotheses, that is, the discrimination function H expressed by thefollowing equation (15), is positive or negative.

$\begin{matrix}{{H(x)} = {{sgn}\left( {\sum\limits_{t = 1}^{T}\;{f_{m}(x)}} \right)}} & (15)\end{matrix}$(4) Face Detection Method

Now, the face detection method in the face detection apparatus 10 shownin FIG. 4 will be described. FIG. 14 is a flowchart showing the facedetection method in the face detection apparatus of the facialexpression recognition system according to an embodiment of thisinvention. First, the image output unit 11 shown in FIG. 4 outputs avariable density image and the integral image generating unit 12generates an integral image expressed by the above-described equation(1) (step S21). This integral image can be formed by repeating anoperation of adding the pixel value of a pixel at the same position inan input image to the sum of pixel values of the pixels above and to theleft of the pixel in the image, sequentially from the upper left part.By using this integral image, it is possible to calculate the sum ofpixel values in a rectangular box at an arbitrary position at a highspeed on the basis of addition or subtraction of the pixels values atthe four corners, as described above. This enables high-speedcalculation of the feature quantity by the discriminator 14 on thesubsequent stage.

Then, the scanning unit 13 vertically and horizontally scans theposition of a search window with respect to the integral image andoutputs a window image (step S22).

The discriminator 14 judges the size of each face and whether therectangular box (window image) is a face image or not at each positionin the image, using the discriminator 14 acquired by the above-describedlearning. As basic procedures for this, similar to the above-describedlearning, each weak hypothesis calculates the feature quantity of theprovided image, and the calculated feature quantity is compared with alearned feature quantity to calculate an estimation value. Every timethis estimation value is calculated, it is multiplied by the reliabilityof the weak hypothesis and the result is added. The resulting value ofsequential weighted addition (i.e., updated value of the value fortaking weighted vote) is used as an evaluation value s. That is, first,the filter output (feature quantity) of the feature quantity filteremployed for the weak hypothesis that is generated first is calculated,using the integral image.

In the case of Adaboost, for each weak hypothesis, the filter output(threshold value) that minimizes the error rate in estimation value withrespect to the learning data set is learned, using the learning dataset, as described above. This threshold value and the filter output ofthe provided window image are compared with each other, and the binaryresult of discrimination about whether the window image is a face imageor non-face image is outputted as the estimation value. This estimationvalue is multiplied by the reliability α of the weak hypothesis and theresult is added. This processing is carried out with respect to theoutput of each weak hypothesis, and whether the provided image is a faceimage or non-face image is judged in accordance with whether the finalsum value (i.e., value for finding a weighted vote) is positive ornegative.

The discriminator 14 in this embodiment has an abort unit (not shown)for performing control to detect a non-face image and abort processingby using the above-described abort threshold value, without waiting forthe results of output of all the weak hypotheses. The processing methodin this discriminator 14 will be described in detail. First, an outputof a filter (rectangle feature quantity) employed for the first weakhypothesis with respect to the current window image is calculated at ahigh speed from an integral image (step S23). Then, the rectanglefeature quantity is compared with a threshold value that has beenlearned in advance for the first weak hypothesis, and the result ofdiscrimination showing whether the current window image is a face imageor not is outputted as an estimation value. Then, it is reflected on anevaluation value s, which is the product of this estimation value andthe reliability of the weak hypothesis (step S24). Next, on the basis ofthis evaluation value s, whether the window image is a detection targetor not and whether or not to abort discrimination are judged.

When a window image is inputted, the evaluation value s is firstinitialized to s=0. Then, estimation values outputted by the individualweak hypotheses of the discriminator are multiplied by theirreliability, and the results are sequentially reflected on theevaluation value s. In the case where the weak hypotheses output binaryvalues as estimation values, if the threshold value for feature quantitydiscrimination by a weak hypothesis t is Tht, and the filter output(rectangle feature quantity) corresponding to the t-th weak hypothesiswith respect to a provided window image is dt, the evaluation value s isexpressed by the following equation (16) using the reliability αt of theweak hypothesis. That is, every time an estimation value is calculated,the product of the estimation value and the reliability is added to theevaluation value s.

$\begin{matrix}\left. {{Evaluation}\mspace{14mu}{value}\text{:}\mspace{14mu} s}\leftarrow{s + \left\{ \begin{matrix}\alpha_{t} & ... & {{Th}_{t} < d_{t}} \\{- \alpha_{t}} & ... & {otherwise}\end{matrix} \right.} \right. & (16)\end{matrix}$

In the case where probability densities or real functions are outputtedas estimation values as in Real Adaboost or Gentleboost, the evaluationvalue s is expressed by the following equation (17). That is, every timean estimation value is calculated, that estimation value is added to theevaluation value s.Evaluation value:s←s+f(d)  (17)

The abort unit of the discriminator 14 judges whether the resulting(updated) evaluation value s is larger than the abort threshold value Rtor not (step S25). If the evaluation value s is smaller than the abortthreshold value Rt at this step S25, it is judged that the currentwindow image is obviously not a face image, and the processing isaborted. Then, the processing goes to step S28. If there is a nextsearch window image, the processing from step S21 is repeated.

On the other hand, if the evaluation value s is larger than thethreshold value Rt, whether or not the processing has been repeated apredetermined number of times (=T times) is judged (step S26). If not,the processing from step S23 is repeated. If the processing has beenrepeated the predetermined number of times (=T times), the processinggoes to step S27, and whether the window image is a detection target ornot is judged in accordance with whether the acquired evaluation value sis larger than 0 or not (step S27). If the evaluation value s is largerthan 0, it is judged that the current window image is a face image ofthe detection target, and its position and size are stored. Then,whether there is a next search window or not is judged (step S28). Ifthere is a next search window, the processing from step S21 is repeated.If the search windows for all the next areas have been scanned, theprocessing goes to step S29 and processing to delete overlapped areas isexecuted.

In this manner, when the discrimination processing for all the windowimages of one input image is completed, the processing shifts to stepS29. In the case of detecting face images of difference sizes, thescanning can be repeated while suitably changing the size of the window.

In the processing after step S29, if areas that are detected as areasindicating a detection target overlap each other in one input image, theoverlapped areas are eliminated. First, whether there area overlappedareas or not is judged. If there are plural areas judged and stored as aface, and these areas are overlapped, the processing goes to step S30.The two overlapped areas are taken out, and the area having a smallerevaluation value s, of these two areas, is regarded as having lowerprobability of being a detection target and is therefore deleted. Thearea having a larger evaluation value s is selected (step S31). Then,the processing from step S29 is repeated. In this manner, one areahaving the highest evaluation value is selected from the areas that areoverlapped plural times and extracted. If two or more detection targetareas are not overlapped, or if there are no detection target areas, theprocessing for one input image ends and the next frame processingstarts. An average value of the overlapped areas may be calculated andoutputted.

With the learning method for the data to be used by the discriminator 14in this embodiment, when generating a weak hypothesis, a filter havinghigh performance can be selected to generate a weak hypothesis withoutsearching all the filters to select a filter having the highestdiscrimination performance, and the learning processing can be carriedout at a high speed without lowering the discrimination performance ofthe weak hypothesis.

Moreover, in this embodiment, as the abort threshold value is learned inadvance, the detection processing can be aborted if it can bediscriminated that a window image is obviously a non-target object, andtherefore the processing in the detection process can be carried out ata very high speed. That is, in the detection process, the value acquiredby multiplying the result of discrimination (estimation value) from theoutput value (feature quantity) of the filter by the reliability of theweak hypothesis used for discrimination is added to the previousevaluation value s, thus sequentially updating the evaluation value s.Every time the evaluation value s is updated, it is compared with theabort threshold value Rt to judge whether or not to continue calculationof the estimation value of the next weak hypothesis. If the evaluationvalue s is less than the abort threshold value, the calculation of theestimation value of the weak hypothesis is aborted and the processingshifts to the next window image. Therefore, redundant calculation can beomitted and real-time high-speed face detection can be carried out. Formost window images, the probability of being a face image is lower andmost window images are non-detection targets. Therefore, by abortingdiscrimination of the window images that are non-detection targets, itis possible to realize a very efficient discrimination process.

In the above-described non-patent reference 1, to realize high-speedprocessing, plural classifiers, each of which includes plural weakhypotheses, are cascaded, and when discrimination by one classifierends, samples having low discrimination scores are judged as non-facesand the processing is aborted at this point. Thus, high-speedcalculation is realized. In this case, since the next classifier usesonly the samples handed over from the previous classifier, that is, thesamples having high discrimination scores, for learning, the problem tobe identified is gradually simplified.

On the other hand, in this embodiment, every time the value acquired bymultiplying the estimation value from each filter output by thereliability, or the quantity of contribution or real function of theestimation value from the filter output, is added, the image is judgedas a non-face, or the abort threshold value for judging whether or notto evaluate the next feature quantity is learned. On the basis of this,control to abort the processing is executed. Therefore, compared withthe above-described non-patent reference 1, the image can be judged as anon-face by using evaluation of estimation values of less weakhypotheses, and the processing in the detection process can be carriedout at a high speed.

In this embodiment, the abort threshold value for aborting the detectionprocessing in the case where it can be judged that an image is obviouslya non-detection target is introduced. However, an abort threshold valuefor aborting detection processing in the case where it can be judgedthat an image is obviously a detection target may be introduced, asdescribed above. Alternatively, these two abort threshold values may beintroduced at the same time.

(5) Facial Expression Recognition Apparatus

The facial expression recognition apparatus will now be described. Theapparatus 20 including the face feature extracting unit 21 and theexpression recognizing unit 22 shown in FIG. 4 identifies whetherinputted face images have specific expressions or not by using specificexpression identifiers for which data have been learned by a method thatwill be described later, on the basis of a Gabor output calculated by amethod that will be described later as a feature quantity, and thusclassifies the inputted face images into seven emotions or expressions.

By combining this facial expression recognition apparatus 20 with theabove-described face detection apparatus, it is possible to realize afacial expression recognition system that performs fully automaticfacial expression recognition. This is different from the conventionaltechnique in that the facial expression recognition is carried out veryaccurately and in real time. For example, in an experiment conducted bythe inventors of this application, generalization performance of 93% wasachieved in the case of 7-way forced choice with respect to new learningsamples.

FIG. 15 is a functional block diagram showing the facial expressionrecognition apparatus 20. As shown in FIG. 15, the facial expressionrecognition apparatus 20 has the face feature extracting unit 21 and theexpression recognizing unit 22 for recognizing an expression from facefeatures extracted by the face feature extracting unit 21. Theexpression recognizing unit 22 has expression identifiers 41 ₁ to 41 ₇(=expression identifiers 41 x) for identifying whether provided data isa specific expression or not, and a expression deciding unit 42 fordeciding and outputting one expression on the basis of the result ofidentification from each expression identifier 41 x.

The face feature extracting unit 21 extracts face features from a faceimage by using a Gabor filter, which is robust against a shift of theimage. Therefore, processing such as clear function detection or innerface feature alignment is not necessary as preprocessing. Since thepreprocessing is not required, the processing time can be largely saved,which is important to real-time applications.

The expression identifiers 41 ₁ to 41 ₇ identify specific expressions ofhappiness, sadness, surprise, disgust, fear, anger, and neutral, astheir respective identification targets, and each of them outputs aresult of identification indicating whether a provided face has thespecific expression or not. Data for the expression identifiers 41 xhave been ensemble-learned by support vector machines (SVMs) or by theabove-described boosting such as Adaboost. Alternatively, by combiningfeature selection based on Adaboost and feature integration based onSVMs, it is possible to learn data so that the expression identifiers 41x can operate accurately and at a high speed.

The expression deciding unit 42 receives, as its input, the result ofdiscrimination by each expression identifier indicating whether aprovided face has the specific expression or not. The expressiondeciding unit 42 employs one of the expression identifiers that has thebest result of discrimination and thus decides one expression. In thecase where the expression identifiers 41 x are constituted by SVMs,discrimination functions are calculated from support vectors learned atthe time of learning, and of these, the discrimination function of thelargest value is outputted as the expression of the face image inputtedfrom the face detection apparatus 10. In the case where the data for theexpression identifiers 41 x have been ensemble-learned by boosting orthe like, an expression having the largest output (hereinafter referredto as discrimination evaluation value) such as the sum of products ofoutputs and reliability of weak hypotheses (value for taking weightedvote), the sum of quantities of contribution, the sum of real functionsor the like, is outputted as the recognized expression. For example,weighted vote is not taken among the expression identifiers 41 x forwhich data have been learned by boosting, because two or moreexpressions may be detected at a time. Also in this case, an expressionhaving the highest discrimination evaluation value can be outputted asthe most likely result.

This facial expression recognition apparatus 20 performs learning forand recognition at each expression identifier 41 x, using a rectangularface box outputted from the face detection apparatus 10, that is, theposition and size of a window image judged as a face image. The methodfor learning data for the facial expression recognition apparatus 20will be described first, and then, the identification method by thefacial expression recognition apparatus 20 will be described.

(6) Facial Expression Learning Method

In learning, first, face images are cut out from a provided imagedatabase, using the above-described face detection apparatus. Learningmay also be carried out using prepared face images. Next, the faceimages are classified into emotion categories as expression recognitiontargets, for example, by a manual operation. In this embodiment, faceimages of a face image group are classified into the above-describedseven emotion categories, and labels corresponding to these categoriesare allocated the face images that have been cut out. Samples aregenerated, each of which is labeled with one of the expressions. In thisembodiment, these samples are used as an expression database forexpression learning. The expression recognizing unit 22 generates(learns) one expression identifier 41 x for each of the seven expressioncategories. Now, the procedure for learning data for the expressionidentifier 41 x related to one expression will be described. Actually,however, data is replaced and learning of data for the expressionidentifier 41 x is repeated X=7 times in order to learn data for theseven expression identifiers 41 x corresponding to the seven emotioncategories, respectively. Although human faces are classified into seventypes of emotions in this embodiment, expressions to be recognized arenot limited to the seven types and data for expression identifierscorresponding to the number of necessary expressions can be learned.

First, in this embodiment, to acquire feature quantities for theexpression identifiers 41 x to identify each expression, Gabor filteringfor extracting face features from face images is carried out, forexample, using 40 types of Gabor filter defined by eight directions andfive frequencies. Gabor filter outputs differ, depending on not only thedirection and frequency but also the pixel position to which the Gaborfilters are applied. In this embodiment, Gabor filters are applied to,for example, an image of 48×48 pixels, and 92160 Gabor outputs areacquired in total.

As the expression identifiers 41 x, either SVMs or Adaboost learners areused. As will be described later, it is possible to provide moreefficient expression identifiers 41 x by SVM-learning only the featurequantities of filters selected by Adaboost from the 92160 filters(features).

For each of the seven expression identifiers 41 x prepared foridentifying the predetermined expressions as recognition targets, alearning operation to output a result indicating whether a provided facehas one expression that is an identification target (hereinafterreferred to as specific expression) is carried out, and then, learning(or training) for the seven expression identifiers 41 x is carried outin order to discriminate each expression from the others. In this case,an emotion category is decided by selecting an expression identifier 41x providing a maximum margin for data that is being learned now.

The learning for the expression recognizing unit 22 is carried out bythree methods. The first learning method is to learn data for SVMs thatperform classification into the emotion categories on the basis of Gaborfilter outputs. The second learning method is to learn data for a finalhypothesis (strong discriminator) for each emotion category, using Gaborfilters as weak hypotheses, in accordance with the above-describedAdaboost algorithm. The third learning method is to repeat theprocessing to select a filter having high discrimination performance togenerate a weak hypothesis from all the Gabor filters by using aboosting technique, and then learn data for SVMs by using only the Gaborfilters selected as weak hypotheses. In this manner, the learningefficiency is improved, compared with the first and second learningmethods. Hereinafter, these three learning methods for expressionidentification will be described.

(6-1) First Learning Method

FIG. 16 is a flowchart showing the first learning method. In any method,the following operations (preprocessing) of steps S31 to S33 are carriedout on a face detection image.

First, learning samples labeled with an expression as a classificationtarget are gathered (step S31). As described above, for example, faceimages detected by the face detection apparatus 10 shown in FIG. 4 areused. These face images are classified, for example, into face imagesjudged as expressing “happiness” and faces images expressing the otheremotions, for example, by a manual operation. A face image groupincluding a group of target expression images representing the targetexpression and a group of non-target expression images representing theother expressions is thus prepared.

Next, since the detected face images have different sizes, each faceimage prepared as described above is resized, for example, toapproximately 48×48 pixels (step S32). Since Gabor filter outputs arerobust against shifts of images, the outputs of face detection can beused without performing particularly fine positioning.

Then, conversion to intensity signal representation is performed, usingGabor filters of eight directions and five scales. In this embodiment,all the 40 types of Gabor filters are applied to all the pixels toacquire filter outputs. The Gabor filters will be later described indetail. In this manner, 40 types of vectors per pixel are provided, thatis, vectors of 48×48 pixels×8 directions×5 scales=92160 dimensions, areprovided per learning sample.

In this embodiment, the three machine-learning methods can be employed,as described above. The first learning method is to learn on the basisof support vector machines (SVMs). First, of the vectors preprocessed atsteps S31 to S33, vectors belonging to the emotion category selected asa learning target are regarded as positive data, and vectors belongingto the other emotion categories are regarded as negative data (stepS34).

Next, using the learning data set including the positive data and thenegative data, support vectors for identifying the positive data and thenegative data are learned (step S35).

SVMs acquire provisional identification functions, using learning datasupplied from outside, that is, an expression learning data setincluding data representing labeled detection targets and non-detectiontargets (also referred to as teacher data or training data). In theidentification, the results of face extraction from inputted face imagesby Gabor filtering are inputted to SVMs. As kernel functions fornon-linearly extending linear identifiers as expression identifiers 41 xby kernel trick, linear, polynomial, RBF kernels with Laplacian, andGaussian basis functions can be used. The inventor of this applicationhas confirmed that the best identification performance is achieved withlinear and RBF kernels using Gaussian basis functions, as will bedescribed later.

To improve identification performance, a boot strap method can beemployed. Images are picked up separately from the images used forlearning, and the picked-up images are used for boot strap. This meansthat when the expression identifier 41 x for which data has been learnedoutputs an erroneous recognition result, the input data can be put intothe learning data set and learning can be performed again.

As a result of this SVM learning, N supports vectors of 92160dimensions, N coefficients α of these support vectors, and labels y ofthe samples that have become support vectors are acquired for eachexpression identifier 41 x corresponding to each emotion category. Theseare saved and will be used at the time of expression recognition, aswill be described later.

In this embodiment, since data for the expression identifiers 41 xcorresponding to the seven emotion categories are learned, as describedabove, learning with respect to all the emotions is performed for eachexpression. When learning with respect to all the emotions is completed(step S36), the processing ends.

(6-2) Second Learning Method

FIG. 17 is a flowchart showing the second learning method for facialexpression recognition. In FIG. 17, preprocessing of steps S41 to S43 issimilar to the processing of steps S31 to S33 shown in FIG. 16. That is,many face images (sample images) are gathered by the face detectionapparatus 10 or the like, and they are classified into seven expressionsas identification targets. Then, all the sample images are resized tothe same size and Gabor filters are applied to all the pixels to acquirefilter outputs. In short, a set of Gabor filter outputs defined by thedirection, frequency, and pixel position to which the filter is applied,is used as a learning model for acquiring the expression identifiers.

Data belonging to an emotion category selected as a learning target areregarded as positive data, and data belonging to the other emotioncategories are regarded as negative data (step S44). Machine-learning isperformed using this expression learning data set.

In the second learning method, boosting is used for machine-learning.While machine-learning using Adaboost will described here, learning mayalso be performed by using the above-described Real Adaboost orGentleboost.

In Adaboost, as weak hypotheses sequentially generated at the time oflearning, 48×48 pixels×8 directions×5 scales=92160 Gabor filter outputsacquired by preprocessing are used. That is, one of the 92160 Gaborfilters is selected and a feature quantity (Gabor filter output) foroutputting an estimation value indicating whether the data of theexpression learning data set are of a discrimination target expressionor non-target expression is learned, thus generating a weak hypothesis.The reliability of the weak hypothesis is thus learned. This learningmethod can be basically similar to the learning method shown in FIG. 11.

First, similar to step S1 of FIG. 11, data weighting is initialized inaccordance with the equation (4) so that the data weighting on eachlearning data of the expression learning data set acquired at step S44as described above is evenly distributed (step S45).

In this embodiment, there are 92160 Gabor filters, that is, 92160filters that can be selected as weak hypotheses. Thus, one of the 92160Gabor filters is selected to generate a weak hypothesis (step S46).

Then, similar to steps S3 and S5, a weighted error rate ε is calculatedin accordance with the equations (5) and (6), and reliability α iscalculated on the basis of the weighted error rate. On the basis of thereliability α, the data weighting on each learning data of theexpression learning data set is updated in accordance with the equation(7) (step S47). As the processing of steps S46 and S47 is repeated anecessary number of times, a necessary number of weak hypotheses aregenerated. Then, learning is continued until a final hypothesis formedby plural learned weak hypotheses perfectly separates the positive dataand the negative data of the expression learning data set and the gapbetween them becomes larger than a predetermined quantity with respectto the size of distribution of these data (step S48). As describedabove, there are 92160 Gabor filter outputs. For example, by learningseveral hundred weak hypotheses, it is possible to classify the learningsamples into positive data and negative data.

In the above-described learning process shown in FIG. 11, the abortthreshold value is calculated in order to realize high-speed processingin discrimination. Also in this method, an abort threshold value foraborting the identification processing on the basis of a judgment that aprovided expression is obviously not the specific expression of theidentification target, or an abort threshold value for aborting theidentification processing on the basis of a judgment that a providedexpression is obviously the specific expression of the identificationtarget, may be learned in advance and used for realizing high-speedprocessing in identification.

Now, the weak hypothesis generation method of step S46 will bedescribed. In generating a weak hypothesis, a filter that minimizes theweighted error rate acquired from data weighting on each learning dataof the expression learning data set at that time is selected, and afeature quantity (in the case of Adaboost, a value to be adiscrimination threshold value) for discriminating whether the data ofthe data set is of the specific expression or not is learned.

As described above, 92160 Gabor filter outputs are acquired for eachlearning sample. With respect to positive data p of i learning samples,the j-th Gabor filter output, of all the Gabor filter outputs J (in thisembodiment, J=92160), is represented by pij. With respect to negativedata n of the i learning samples, the j-th Gabor filter of the 92160Gabor filter outputs is represented by nij.

First, histograms are formed by multiplying each the positive data p andthe negative data n of the j-th Gabor filter output by data weighting Diof Adaboost. FIG. 18 is a graph showing the histograms. That is, in FIG.18, the horizontal axis represents the j-th Gabor filter output, and thevertical axis represents the number of positive data p or negative datan in the j-th Gabor filter output. In FIG. 18, a solid line shows ahistogram P of the positive data p and a broken line shows a histogram Nof the negative data n.

Next, identification of the positive data p or the negative data n iscarried out using a search value th for searching for a threshold valueTh. The sum of weighted count values of the positive data p at and abovethe search value th is represented by pl, and the sum of weighted countvalues of the positive data p below the search value th is representedby ps. The sum of weighted count values of the negative data n at andabove the search value th is represented by nl, and the sum of weightedcount values of the negative data n below the search value th isrepresented by ns. Using these values pl, ps, nl, ns and the searchvalue th, the identification error e can be calculated by the followingequation (18).

$\begin{matrix}\begin{matrix}{{e_{j}\left( T_{h} \right)} = {\min\left( {\frac{{ps} + {nl}}{{ps} + {pl} + {ns} + {nl}},\frac{{pl} + {ns}}{{ps} + {pl} + {ns} + {nl}}} \right)}} \\{= {\min\left( {\frac{{ps} + {nl}}{{ps} + {pl} + {ns} + {nl}},{1 - \frac{{ps} + {nl}}{{ps} + {pl} + {ns} + {nl}}}} \right)}}\end{matrix} & (18)\end{matrix}$

Specifically, the search value th is shifted in the direction of thehorizontal axis represented by the j-th Gabor filter output, and thesearch value th that minimizes the error e is found. This search valueth that minimizes the error e is used as the threshold value Th(j) ofthis Gabor filter output. As shown in the upper part of the equation(18), error ej(th) is the smaller one of the correct answer rate((ps+nl)/(ps+pl+ns+nl)) and the incorrect answer rate((pl+ns)/(ps+pl+ns+nl)) of all the answers. However, as shown in thelower part of the equation (18), when the search value th is changed,the sum pl of weighted count values of the positive data of correctanswers and the sum ns of weighted count values of negative data ofcorrect answers increase or decrease by the amount of the shifted searchvalue th. Therefore, all pl and ns need not be counted for each searchvalue th, and the processing can be carried out at a high speed.

In this manner, the error ej(Th) is calculated for all the J Gaborfilter outputs, and one weak hypothesis that provides the least errorej(Th) is employed. This error ej(Th) is the error rate of the weakhypothesis.

The weak hypothesis generation method shown in FIG. 12 may be applied,for example, to a case where face images used for learning have a verylarge number of pixels, requiring many filters. Specifically, filtersare selected a predetermined rate from all the selectable filters, andof the selected filters, one or plural high-performance filters havinghigh discrimination performance are selected. Then, new filters aregenerated by adding a predetermined modification to the high-performancefilters. Of the high-performance filters and the new filters, a filterhaving the best discrimination performance, that is, a filter thatminimizes the above-described error ej(Th), is selected to generate aweak hypothesis. In this case, the new filters can be generated, forexample, by changing the frequencies and directions of the filtersselected as high-performance filters or by shifting the pixel positionby one.

It is also possible to select filters from all the selectable filters ata predetermined rate, generate new filters from the selected filters,and select one filter having the best discrimination performance fromthe selected filters and new filters so as to generate a weakhypothesis.

Using the error ej(Th) of the weak hypothesis selected in this manner onthe basis of the Adaboost learning method, the reliability of the weakhypothesis is calculated as described at step S47, and the dataweighting Di on learning data i is updated in accordance with thecorrect answer or incorrect answer of the weak hypothesis. Thisprocessing is repeated.

Next, when the expression identifier 41 x based on the sum of T weakhypotheses acquired as described above is applied to the learningsamples, if the positive data and the negative data are separated with asufficient margin, learning is aborted at this point (step S48). Theexpression identifier 41 x is adapted for discriminating whether aprovided expression is an identification target expression or non-targetexpression on the basis of the result of multiplication and addition ofthe outputs of the T weak hypotheses and their reliability. At the timeof identification, which will be described later, unlike theabove-described face detection, each expression identifier 41 x outputsa sum value acquired by sequentially adding the products of outputs andreliability of the weak hypotheses, instead of taking a weighted votefrom the sum value of the products of outputs and reliability of theweak hypotheses. Thus, for example, when the outputs of two expressionidentifiers 41 x show positive values, the expression deciding unit 42can employ the result of the expression identifier 41 x with a largersum value and output it as the result of identification. If the positivedata and the negative data cannot be separated sufficiently, theprocessing goes back to step S46 and a new weak hypothesis is generated.In this embodiment, a final hypothesis can be provided by selectingapproximately 1/200 of all the Gabor filters (92160 Gabor filters) togenerate weak hypotheses.

As a result of the above-described learning, the directions and scalesof the selected weak hypotheses, that is, the Gabor filters, theinformation about image position (pixel position), the output values ofthe filters (feature quantities), and the reliability α of the weakhypotheses are acquired. These are saved and will be used forrecognition, which will be described later.

(6-3) Third Learning Method

The identifiers for which data are learned by the first learning methodusing SVMs have non-linearity based on kernels and therefore haveexcellent performance. However, it is necessary to calculate, forexample, vectors of 92160 dimensions and the calculation time fordiscrimination may be longer than in the case of the expressionidentifiers 41 x for which data is learned by boosting of the secondlearning method. Thus, in the third learning method, in order to reducethe calculation time for discrimination, SVM learning (hereinafter alsoreferred to as AdaSVM) is performed using only the feature quantities(Gabor filters) employed in Adaboost learning.

In this third learning method, first, a data set is prepared whichincludes weighted specific expression face image data representing aspecific expression and weighted non-specific face image datarepresenting expressions different from the expression shown by thespecific expression face image, and from plural Gabor filters, a Gaborfilter having a minimum error rate in discriminating the specificexpression face image data and the non-specific expression face imagedata is selected as a first weak hypothesis. Then, reliability of thisfirst weak hypothesis with respect to the data set is calculated, andthe weighting on the specific expression face image data and thenon-specific expression face image data is updated on the basis of thereliability.

Next, of the plural Gabor filters, a Gabor filter having a minimum errorrate in discriminating the specific expression face image data and thenon-specific expression face image data with the updated weighting isselected as a second weak hypothesis.

In this manner, support vectors are learned by SVMs to which featurequantities of the specific expression face image data and thenon-specific expression face image data extracted by at least the Gaborfilters selected as the first weak hypothesis and the second weakhypothesis, and a hypothesis (expression identifier) for discriminatingthe specific expression face image data and the non-specific expressionface image data is generated. This third learning method will now bedescribed in detail.

FIG. 19 is a flowchart showing the third learning method for faceexpression recognition. In FIG. 19, preprocessing of steps S51 to S53 issimilar to the processing of steps S31 to S33 shown in FIG. 16.

Then, data belonging to an emotion category selected as a learningtarget are regarded as positive data, and data belonging to the otheremotion categories are regarded as negative data (step S54).Machine-learning is carried out using this expression learning data set.

First, Adaboost learning is executed (step S55). The processing of thisstep S55 is similar to the processing of steps S45 to S48 of theabove-described second method. That is, first, as weak hypotheses aresequentially generated, combinations of frequencies and directions ofGabor filters and pixel positions in the sample image are sequentiallylearned. At this step S55, for example, approximately 538 filters areselected from all the Gabor filter outputs (92160 Gabor filter outputs),that is, approximately 1/200 of the filters is selected, until a finalhypothesis is acquired. In this manner, in Adaboost, if approximately1/200 of the 92160 filters is selected to generated weak hypotheses, anidentifier for identifying whether a provided expression is the targetexpression or non-target expression can be generated. At this step S55,when the negative data and the positive data of the learning data setare perfectly separated and the gap between them becomes larger than apredetermined quantity with respect to the size of distribution of thesedata, learning is stopped.

Next, SVM learning is carried out using only the outputs of the Gaborfilters employed for weak hypotheses generated by boosting learning ofstep S55. First, using only the Gabor filters employed for weakhypotheses in Adaboost, each learning face image labeled with apredetermined expression is filtered to extract face features.Therefore, while support vectors must be learned from the92160-dimensional vectors in the first learning method, in this thirdlearning method, support vectors are learned from, for example,538-dimensional vectors, which is approximately 1/200 of the92160-dimensional vectors. That is, SVM learning is carried out usingthe 538-dimensional vectors as new learning data. This enableshigh-speed calculation both in learning and in identification. Asboosting is combined with SVMs for learning, generalization performanceimproves.

As a result of learning, the directions and scales of the Gabor filtersemployed for generated weak hypotheses, and information about pixelpositions, are acquired. If the number of weak hypotheses is T, supportvectors of T-dimensional Gabor filter outputs, their coefficients a, andlabels y of the corresponding learning samples are saved and will beused in recognition, which will be described later.

Gabor filtering and SVMs will now be described in detail.

(6-4) Gabor Filtering

It is already known that human visual cells include cells havingselectivity with respect to specific orientations. These cells are cellsthat respond to vertical lines and cells that respond to horizontallines. Similarly, Gabor filtering is based on a spatial filter formed byplural filters having orientation selectivity.

A Gabor filter is spatially represented by a Gabor function. A Gaborfunction g(x,y) is constituted by a carrier s(x,y) consisting of acosine component and an envelope wr(x,y) in the form of two-dimensionalGaussian distribution, as expressed by the following equation (19)g(x,y)=s(x,y)w _(r)(x,y)  (19)

The carrier s(x,y) is expressed as in the following equation (20), usingcomplex numbers. In this equation, the coordinate value (u0, v0)represents the spatial frequency and P represents the phase of thecosine component.s(x,y)=exp(j(2π(u ₀ x+v ₀ y)+P))  (20)

The carrier s(x,y) shown in the equation (20) can be split into a realcomponent Re(s(x,y)) and an imaginary component Im(s(x,y)), as expressedby the following equation (21).

$\begin{matrix}\left\{ \begin{matrix}{{{Re}\left( {s\left( {x,y} \right)} \right)} = {\cos\left( {{2{\pi\left( {{u_{0}x} + {v_{0}y}} \right)}} + P} \right)}} \\{{{Im}\left( {s\left( {x,y} \right)} \right)} = {\sin\left( {{2{\pi\left( {{u_{0}x} + {v_{0}y}} \right)}} + P} \right)}}\end{matrix} \right. & (21)\end{matrix}$

On the other hand, the envelope of two-dimensional Gaussian distributionis expressed by the following equation (22).w _(r)(x,y)=K exp(−π(α²(x−x ₀)_(r) ² +b ²(y−y ₀)_(r) ²))  (22)

In this equation, the coordinate value (x0,y0) represents the peak ofthis function, and constants a and b are scale parameters of Gaussiandistribution. The subscript r indicates a rotating operation asexpressed by the following equation (23).

$\begin{matrix}\left\{ \begin{matrix}{\left( {x - x_{0}} \right)_{r} = {{\left( {x - x_{0}} \right)\cos\;\theta} + {\left( {y - y_{0}} \right)\sin\;\theta}}} \\{\left( {y - y_{0}} \right)_{r} = {{{- \left( {x - x_{0}} \right)}\sin\;\theta} + {\left( {y - y_{0}} \right)\cos\;\theta}}}\end{matrix} \right. & (23)\end{matrix}$

Therefore, a Gabor filter is expressed as a spatial function as shown inthe following equation (24) based on the equations (20) and (22).g(x,y)=K exp(−π(α²(x−x ₀)_(r) ² +b ²(y−y)_(r) ²)) exp(j(2π(u ₀ x+u ₀y)+P))  (24)

The face feature extracting unit 21 of this embodiment carries out faceextraction processing using 40 Gabor filters in total in eightdirections and five spatial frequencies. FIGS. 20A and 20B show modelsin the spatial domain of Gabor filters used in this embodiment. FIG. 20Ashows examples of Gabor filters of different frequency components. FIG.20B shows eight directions of the Gabor filters. The density in FIGS.20A and 20B corresponds to a component in the direction of thecoordinate axis orthogonal to the sheet.

The response of a Gabor filter is expressed by the following equation(25), where Gi represents the i-th Gabor filter, Ji represents theresult of the i-th Gabor filter (Gabor Jet) and I represents the inputimage. Actually, the equation (25) can be calculated at a high speed byusing fast Fourier transform.J _(i)(x,y)=G _(i)(x,y)

I(x,y)  (25)

That is, for example, when a learning sample including 48×48 pixels isused, 48×48=2304 outputs are acquired as Gabor Jets Ji from the i-thGabor filter.

To examine the performance of the prepared Gabor filter, the imageacquired by filtering is reconstructed. The reconstructed image H isexpressed by the following equation (26).

$\begin{matrix}{{H\left( {x,y} \right)} = {\sum\limits_{i = 1}^{n}\;{a_{i}{J_{i}\left( {x,y} \right)}}}} & (26)\end{matrix}$

Then, an error E of the reconstructed image H with respect to the inputimage I is expressed by the following equation (27).

$\begin{matrix}\begin{matrix}{E = {\frac{1}{2}{{{I\left( {x,y} \right)} - {H\left( {x,y} \right)}}}^{2}}} \\{= {\frac{1}{2}{\sum\limits_{x,y}\;\left( {{I\left( {x,y} \right)} - {H\left( {x,y} \right)}} \right)^{2}}}} \\{= {\frac{1}{2}{\sum\limits_{x,y}\;\left( {{I\left( {x,y} \right)} - {\sum\limits_{i = 0}^{Q}\;{a_{i}{J_{i}\left( {x,y} \right)}}}} \right)^{2}}}} \\{= {\frac{1}{2}{\sum\limits_{x,y}\;\left( {{I\left( {x,y} \right)} - {\sum\limits_{i = 0}^{Q}\;{a_{i}G_{i} \times I}}} \right)^{2}}}}\end{matrix} & (27)\end{matrix}$

As an optimum parameter a that minimizes this error E is found, the Himage can be reconstructed and the performance of the Gabor filter canbe examined.

(6-5) Support Vector Machines

SVMs will now be described. SVMs are considered to have the highestlearning generalization performance in the field of pattern recognition.Using SVMs, whether a facial expression is a certain expression or notis identified.

SVMs are described, for example, in B. Sholkopf, C. Burges, A. Smola,“Advance in Kernel Methods Support Vector Learning,” The MIT Press,1999. The result of the preliminary experiment conducted by theinventors shows that the recognition method using SVMs provides betterresults than principal component analysis (PCA) and techniques usingneural networks.

The SVM technique is a technique of classifying a provided data set intotwo classes, as expressed by the following equation (28). In this case,if a data set belongs to class A, y is 1. If a data set belongs to classB, y is −1. It is assumed that a sample x belongs to a set R(N) ofN-dimensional real vectors.y=f(x), xε R(N),y=±1  (28)

SVMs are learners using linear identifiers (perceptrons) for theidentification function f and can be extended to a non-linear space byusing kernel functions. In learning the identification function, amaximum margin for class separation is taken and its solution isacquired by solving a quadratic mathematical planning problem.Therefore, it can be theoretically guaranteed that a global solution canbe reached.

Normally, the problem of pattern recognition is to find theidentification function f of the following equation (29) with respect totest samples x =(x1, x2, . . . , xn).

$\begin{matrix}{{{f(x)} = {{{\sum\limits_{j = 1}^{n}{w_{j}x_{j}}} + b} = w}}{{\cdot x} + b}} & (29)\end{matrix}$

parameter w_(j): weighting of linear identifier

parameter b: bias term

w: weighting vector

A set of points satisfying f(x)=0 of this identifier (i.e.,identification plane) is a (d-1)-dimensional hyperplane L. As shown inFIG. 21, an identification plane for identifying class A indicated by ∘and class B indicated by □ in an SVM is the hyperplane L passing themiddle between class A and class B.

The class labels (teacher labels) of learning samples (vector x) forSVMs are expressed by the following equation (30)y=(y1,y2, . . . , yn)  (30)

Since the parameters w and b have redundancy, if a restriction that|w×x+b| (where w and x are vectors) of the equation (29) is 1 is addedto a sample that is closest to the hyperplane, face pattern recognitionin SVMs can be considered to be a problem of minimizing the square ofthe weighting element w under the restricting condition expressed by thefollowing formula (31).y _(i)(w·x+b)≧1  (31)

The problem with such a restriction can be solved by using theLagrange's undefined constant method. That is, the Lagrange's expressedby the following equation (32) is first introduced.

$\begin{matrix}{{L\left( {w,b,\alpha} \right)} = {{\frac{1}{2}{w}^{2}} - {\sum\limits_{j = 1}^{l}{\alpha_{i}\left( {y_{i}\left( {\left( {{w \cdot x_{i}} + b} \right) - 1} \right)} \right)}}}} & (32)\end{matrix}$

Next, each of b and w is partially differentiated, as expressed by thefollowing equation (33).

$\begin{matrix}{{\frac{\partial L}{\partial b} = {\frac{\partial L}{\partial w} = {\left. 0\rightarrow{\sum\limits_{i = 1}^{l}{\alpha_{i}y_{i}}} \right. = 0}}},{w = {\sum\limits_{i = 1}^{l}{\alpha_{i}y_{i}x_{i}}}}} & (33)\end{matrix}$

As a result, face pattern identification in SVMs can be considered to bea quadratic planning problem expressed by the following formula (34).

$\begin{matrix}{{\max\limits_{\alpha}{\sum\limits_{i = 1}^{l}\alpha_{i}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{l}{\alpha_{i}\alpha_{j}y_{i}y_{j}x_{i}^{T}x_{j}}}}} & (34)\end{matrix}$

restricting condition: α_(i)≧0, Σα_(i) y_(i)=0

In the case where the number of dimensions in the feature space is lessthan the number of samples, a slack variable ξ≧0 is introduced in orderto relax the restricting condition, and the restricting condition ischanged as expressed in the following formula (35).y _(i)(w·x _(i) +b)≧1−ξ_(i ξ÷)0, i=1, . . . l  (35)

For optimization, the objective function of the following formula ( 36)is minimized.

$\begin{matrix}{{\frac{1}{2}{w}^{2}} + {C{\sum\limits_{i = 1}^{l}\xi_{i}}}} & (36)\end{matrix}$

In the formula (36), C is a coefficient designating the extent to whichthe restricting condition should be relaxed and its value must bedecided experimentally. The problem related to the Lagrange's constant ais changed as expressed by the following formula (37).

$\begin{matrix}{{\max\limits_{\alpha}{\sum\limits_{i = 1}^{l}\alpha_{i}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{l}{\alpha_{i}\alpha_{j}y_{i}y_{j}x_{i}^{T}x_{j}}}}} & (37)\end{matrix}$

restricting condition: 0≦α_(i)≦C, Σα_(i) y_(i)=0

However, the formula (37) itself cannot solve the non-linear problem.Thus, in this embodiment, a kernel function K is introduced to carryingout mapping in a high-dimensional space (kernel trick) and linearseparation is carried out in that space. Therefore, it is equivalent tonon-linear separation in the original space.

The kernel function is expressed by the following equation (38) using acertain map Φ.K(x,y)=Φ(x)Φ(y)  (38)

The identification function f of the equation (29) can also be expressedby the following equation (39).

$\begin{matrix}\begin{matrix}{{f\left( {\Phi(x)} \right)} = {{\sum\limits_{i = 1}^{l}{\alpha_{i}y_{i}{\Phi(x)}^{T}{\Phi\left( x_{i} \right)}}} + b}} \\{= {{\sum\limits_{i = 1}^{l}\;{\alpha_{i}y_{i}{K\left( {x,x_{i}} \right)}}} + b}}\end{matrix} & (39)\end{matrix}$

Moreover, learning can be considered to be the quadratic planningproblem expressed by the following formula (40).

$\begin{matrix}{{\max\limits_{\alpha}{\sum\limits_{i = 1}^{l}\alpha_{i}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{l}{\alpha_{i}\alpha_{j}y_{i}y_{j}{K\left( {x_{i},x_{j}} \right)}}}}} & (40)\end{matrix}$

restricting condition: 0≦α_(i)≦C, Σα_(i) y_(i)=0

As the objective function si minimized under the restricting conditionexpressed by the formula (40), the identification function f of theequation (29) can be calculated as expressed by the following equation(41).

$\begin{matrix}{{{f(x)} = {{sgn}\left( {{\sum\limits_{i = 1}^{l}{\alpha_{i}y_{i}{K\left( {x_{i},x} \right)}}} + b} \right)}}{b = {- {\sum\limits_{i = 1}^{l}\;{\alpha_{i}y_{i}{K\left( {x_{i},x} \right)}}}}}} & (41)\end{matrix}$

As exemplary kernel functions, for example, polynomial kernel, sigmoidkernel, and Gaussian kernel (RBF or radius basic function) expressed bythe following equations (42) to (44) can be used.

$\begin{matrix}{{K\left( {x,y} \right)} = \left( {{x \cdot y} + 1} \right)^{p}} & (42) \\{{K\left( {x,y} \right)} = {\tanh\left( {{{ax} \cdot y} + b} \right)}} & (43) \\{{K\left( {x,y} \right)} = {\exp\left( {- \frac{{{x - y}}^{2}}{\alpha^{2}}} \right)}} & (44)\end{matrix}$(7) Facial Expression Recognition Method

The facial expression recognition method will now be described. Asdescribed above, the learning methods for the expression recognizingunit 22 includes the first method of SVM-learning Gabor filter outputsfor each expression identifier 41 x constituting the expressionrecognizing unit 22, the second method of learning Gabor filter outputsby boosting, and the third method of selecting some of all the Gaborfilters by boosting and SVM-learning their outputs. Recognition methodsin the expression recognizing unit 22 acquired by these three learningmethods will be described hereinafter as first to third recognitionmethods.

(7-1) First Recognition Method (Gabor Filter with SVM)

First, the first recognition method will be described. An input imagefrom an image pickup unit such as a camera is inputted to the facedetection apparatus 10 shown in FIG. 4 and a face image is detected bythe above-described method. When a face is found in the input image, theimage at the position of the face is cut out and inputted to the facialexpression recognition apparatus 20.

Next, as in the case of learning, the face image is resized to 48×48pixels. The resized face image is supplied to the face featureextracting unit 21, and 92160-dimensional Gabor filter outputs aregenerated by using Gabor filters. The Gabor filter outputs are suppliedto the expression recognizing unit 22. The expression recognizing unit22 is adapted for classifying face images into seven expressions and hasthe expression identifiers 41 x corresponding to the seven expressionsto be identified, respectively. The Gabor filter outputs are inputted tothe seven expression identifiers 41 x and each expression identifier 41x identifies whether the expression of the face is a specific expressionas an identification target or an expression different from the specificexpression.

Discrimination function outputs are acquired with respect to the sevenexpression identifiers 41 x based on SVM learning. Each of theexpression identifiers 41 x has acquired N support vectors, Ncoefficients α and labels y of the individual support vectors fromlearning, and finds the result of recognition from the identificationfunction of the equation (39) using the Gaussian kernel function of theequation (44). In this operation, 92160-dimensional kernel functioncalculation is carried out N times. Then, the expression deciding unit42 shown in FIG. 15 outputs an expression that is the identificationtarget of the expression identifier 41 x having the largest value of theidentification results (discrimination function outputs) of the sevenexpression identifiers 41 x, as the result of judgment of the facialexpression recognition apparatus 20.

(7-2) Second Recognition Method (Gabor Filter with Adaboost)

Next, the second recognition method will be described. As in the firstrecognition method, a face image detected and cut out by the facedetection apparatus 10 is inputted and this face image is resized to48×48 pixels. Then, discrimination function outputs are acquired withrespect to the seven expression identifiers 41 x based on Adaboostlearning of the above-described second learning method. Thediscrimination function H is expressed by the following equation (45).

$\begin{matrix}{{H(x)} = {\quad{\sum\limits_{t = 1}^{T}\;{\alpha_{t}{h_{t}(x)}}}}} & (45)\end{matrix}$

In accordance with a Gabor filter selected by Adaboost learning, a weakhypothesis that outputs ht in the equation (45) is decided. That is, theequation (23) is determined in accordance with the direction of theselected Gabor filter, and the scale parameter of the equation (22) isdecided from the scale of the selected Gabor filter. A Gabor kernel isthus acquired.

The result of application of this Gabor kernel to an image around aselected pixel (Gabor filter output) is discriminated by using thethreshold value Th calculated in learning. The result of discriminationfrom which its sign (sgn) has been removed is the output ht of the weakhypothesis. This output is multiplied by the reliability α of the weakhypothesis decided in learning, and the result is added. Thiscalculation is carried out for all the weak hypotheses to acquireoutputs of discrimination functions H (sum value for taking weightedvote). Then, the expression deciding unit 42 shown in FIG. 15 outputsthe largest one of the outputs of discrimination functions H of theseven expression identifiers 41 x, as the expression of the input faceimage. The discrimination function H may discriminate whether theexpression of the input face is the expression regarded as theidentification target by the expression identifier 41 x in accordancewith weighted vote (with respect to whether the sign of the equation(45) is positive or negative) acquired in each expression identifier 41x. However, for example, in the case of identifying plural expressionsby plural expression identifiers 41 x, two or more expressionidentifiers 41 x can identify expressions simultaneously. That is, theoutputs of discrimination functions H in two or more expressionidentifiers 41 x can be positive. In such a case, the expression of thelarger output value of discrimination function H, which is the sum valueof multiplied and added weighting, is used as the result of recognition.

(7-3) Third Recognition Method (Gabor Filter with Adaboost and SVM)

Next, the third recognition method will be described. As in the firstrecognition method, a face image detected and cut out by the facedetection apparatus 10 is inputted and this face image is resized to48×48 pixels. Then, discrimination function outputs are acquired withrespect to the seven expression identifiers 41 x based on the learningof the above-described third learning method (hereinafter referred to asAdaSVM).

First, using a Gabor filter selected by AdaSVM learning, vectors ofdimensions corresponding to the number of filters employed for weakhypotheses generated by Adaboost learning are generated from the inputimage. That is, the Gabor filter acquired in accordance with theequations (22) and (23) for one of the scale and direction selected bythe above-described Adaboost learning is applied to an image around aselected pixel selected by the same learning, and one filter output isthus acquired. This operation is repeated a number of timescorresponding to the number of filters, thus generating input vectorscorresponding to the number of filters.

Then, using the support vectors of the filter outputs, theircoefficients and labels, acquired by SVM learning of AdaSVM learning,the input vectors are substituted into the equations (44) and (39) toacquire discrimination function outputs f. Then, the expression decidingunit 42 outputs an expression of the largest one of the outputs ofdiscrimination functions H of the seven expression identifiers 41 x, asthe expression of the input face.

Since such a facial expression recognition apparatus 20 uses Gaborfilters robust against shifts of images, it can carry out expressionrecognition without performing processing such as positioning of theresult of face detection and can recognize a facial expression at a highspeed.

As identification can be made by SVMs using Gabor filter outputs asfeature quantities, seven expressions can be accurately identified.Similarly, as expressions are identified by using plural weak hypothesesgenerated by boosting using Gabor filter outputs as feature quantities,recognition can be carried out at a higher speed.

Moreover, if only a filter selected in learning based on Adaboostlearning using Gabor filter outputs as feature quantities is used, andexpression identification is carried out by SVMs with vectors of reduceddimensions, arithmetic processing in learning and recognition can bereduced and high-speed processing can be realized. If Adaboost and SVMsare combined for learning, generalization errors can be reduced furtherand generalization performance can be improved.

Furthermore, while learning and identification are carried out with faceimages rescaled 48×48 pixels in this embodiment, increase in resolutionenables further improvement in performance.

By combining this face recognition with the above-described facedetection apparatus 10, it is possible to detect faces in real time frominputted dynamic images or the like and to recognize the expressions ofthe detected face images.

(8) Other Embodiments

The facial expression recognition system in this embodiment can cut outface areas from input images in real time and classify facialexpressions. Therefore, if this facial expression recognition system isprovided on a robot apparatus of various purposes such as entertainmentand nursing, real-time interaction between humans and the robotapparatus is possible. The robot apparatus, equipped with this facialexpression recognition system, can recognize facial expressions of usersand thus can carry out new emotional expressions to the users. Moreover,if such a facial expression recognition system is interlocked with anapparatus having an animation generation and display function, theapparatus can recognize facial expressions of humans and displayanimations responding to the facial expressions.

Such a robot apparatus or animation generation apparatus can understandfacial expressions of users and show certain responses in accordancewith the facial expressions of the users. For example, when the user'sexpression of “happiness” is recognized, the robot apparatus cansimilarly shows the expression of “happiness” or the animation apparatuscan display an animation representing the expression of “happiness”.When the user's expression of “sadness” is recognized, the apparatus canreact to cheer up the user.

In this manner, the facial expression recognition system in thisembodiment can automatically recognize facial expressions and can beeasily used on the basis facial expressions as action measurementcriteria. As detailed analysis of dynamic changes of faces is madepossible, which was impossible in the conventional technique, it hassignificant effects on basic research. A computer system having suchcapability can be broadly used in various fields of basic and appliedresearch such as man-machine communications, security, law enforcement,psychiatry, education, and telecommunications.

(9) Robot Apparatus

A specific example of the robot apparatus equipped with theabove-described facial expression recognition system will now bedescribed. In this embodiment, a two-legged walking robot apparatus isdescribed as an example. However, the system can be applied not only toa two-legged walking robot apparatus but also a four-legged, wheeled orotherwise movable robot apparatus.

This humanoid robot apparatus is a practical robot that assists humanactivities in living environment and various situations of daily life.It is an entertainment robot that can act in accordance with itsinternal state (anger, sadness, joy, pleasure, etc.) and can alsoexhibit basic actions of humans. It is adapted for exhibiting actions inaccordance with facial expressions of users recognized by theabove-described facial expression recognition system. FIG. 22 is aperspective view showing an outlook of the robot apparatus in thisembodiment.

As shown in FIG. 22, a robot apparatus 101 is constructed by connectinga head unit 103, left and right arm units 104R, L, and left and rightleg units 105R, L to predetermined positions on a trunk unit 102. (R andL are suffixes representing right and left, respectively. These suffixeswill be similarly used hereinafter.) FIG. 23 schematically shows a jointdegree-of-freedom structure of the robot apparatus 101. The neck jointsupporting the head unit 103 has three degrees of freedom based on aneck joint -yaw shaft 111, a neck joint pitch shaft 112 and a neck jointroll shaft 113.

Each of the arm units 104R, L forming the upper limbs has a shoulderjoint pitch shaft 117, a shoulder joint roll shaft 118, an upper arm yawshaft 119, an elbow joint pitch shaft 120, a forearm yaw shaft 121, awrist joint pitch shaft 122, a wrist joint roll shaft 123, and a handpart 124. The hand part 124 is actually a multi-joint multi-degree offreedom structure including plural fingers. However, since theoperations of the hand part 124 provide less contribution to or effectson attitude control or walking control of the robot apparatus 101, tosimplify the explanation, the hand part 124 is assumed to have zerodegree of freedom in this specification. Therefore, each arm has sevendegrees of freedom.

The trunk unit 102 has three degrees of freedom based on a trunk pitchshaft 114, a trunk roll shaft 115 and a trunk yaw shaft 116.

Each of the leg units 105R, L forming the lower limbs has a hip jointyaw shaft 125, a hip joint pitch shaft 126, a hip joint roll shaft 127,a knee joint pitch shaft 128, an ankle joint pitch shaft 129, an anklejoint roll shaft 130, and a foot part 131. In this specification, thepoint of intersection between the hip joint pitch shaft 126 and the hipjoint roll shaft 127 defines the position of the hip joint of the robotapparatus 101. The human foot part 131 is actually a structure includinga multi-joint multi-degree of freedom sole. However, in thisspecification, the sole of the robot apparatus 101 is assumed to havezero degrees of freedom in order to simplify the explanation. Therefore,each leg has six degrees of freedom.

To summarize the above-described structure, the robot apparatus 101 has3+7×2+3+6×2=32 degrees of freedom in total. However, the robot apparatusfor entertainment is not necessarily limited to the 32 degrees offreedom. In accordance with restrictions in design and production andrequired specifications, the number of degrees of freedom, that is, thenumber of joints, can be increased or decreased appropriately.

The degrees of freedom of the robot apparatus 101 as described above areactually provided by using an actuator. Since elimination of unwantedbulges on the appearance, formation of a shape close to the naturalshape of a human body, and attitude control of the two-legged unstablestructure are demanded, it is preferred that the actuator is small-sizedand light-weight.

In such a robot apparatus, a control system for controlling theoperations of the whole robot apparatus is provided in the trunk unit102 or the like. FIG. 24 is a schematic view showing the control systemstructure of the robot apparatus 101. As shown in FIG. 24, the controlsystem includes a thought control module 300 for dynamically respondingto user inputs or the like and controlling judgment of emotions andexpression of emotions, and an action control module 400 for controllinggeneral coordination of the robot apparatus 101 such as driving ofactuators 450.

The thought control module 300 includes a central processing unit (CPU)311 for executing arithmetic processing related to judgment andexpression of emotions, a random access memory (RAM) 312, a read-onlymemory (ROM) 313, and an external storage device (hard disk drive or thelike) 314. The thought control module 300 is an independently driveninformation processing device capable of performing self-completeprocessing within the module.

This thought control module 300 decides the current emotion and will ofthe robot apparatus 101 in accordance with external stimulations such asimage data inputted from an image input device 351 and audio datainputted from an audio input device 352. That is, it can recognize auser's facial expression from inputted image data and reflect thisinformation on the emotion and will of the robot apparatus 101 so as toexhibit an action corresponding to the user's facial expression, asdescribed above. The image input device 351 has, for example, plural CCD(charge-coupled device) cameras. The audio input device 352 has, forexample, plural microphones.

The thought control module 300 issues commands to the action controlmodule 400 to execute operation or action sequences based on thedecision of the will, that is, movement of the four limbs.

The action control module 400 includes a CPU 411 for controlling generalcoordination of the robot apparatus 101, a RAM 412, a ROM 413, and anexternal storage device (hard disk drive or the like) 414. The actioncontrol module 400 is an independently driven information processingdevice capable of performing self-complete processing within the module.In the external storage device 414, for example, walking patternscalculated off-line, target ZMP orbit, and other action plans can bestored.

Various devices such as actuators 450 for realizing the degrees offreedom of the joints dispersed in the whole body of the robot apparatus101 shown in FIG. 23, a distance measuring sensor (not shown) formeasuring the distance from a target object, an attitude sensor 451 formeasuring the attitude and inclination of the trunk unit 102, groundingconfirmation sensors 452, 453 for detecting takeoff or landing of theleft and right soles, load sensors provided on the soles 131, and apower control device 454 for controlling the power supply such as abattery, are connected to the action control module 400 via a businterface (I/F) 401. The attitude sensor 451 is formed, for example, bya combination of an acceleration sensor and a gyro sensor. Each of thegrounding confirmation sensors 452, 453 is formed by a proximity sensor,micro switch or the like.

The thought control module 300 and the action control module 400 areconstructed on a common platform and are interconnected via businterfaces 301, 401.

In the action control module 400, the actuators 450 control generalcoordination of the body in order to exhibit an action designated by thethought control module 300. Specifically, the CPU 411 takes out anoperation pattern corresponding to the action designated by the thoughtcontrol module 300 from the external storage device 414, or internallygenerates an operation pattern. Then, the CPU 411 sets foot movement,ZMP orbit, trunk movement, upper limb movement, horizontal position andheight of waist and the like in accordance with the designated operationpattern, and transfers a command value designating an operationcorresponding to these settings to each actuator 450.

The CPU 411 also detects the attitude and inclination of the trunk unit102 of the robot apparatus 101 from an output signal of the attitudesensor 451 and detects whether the leg units 105R, L are in an idlingstate or standing state from output signals of the groundingconfirmation sensors 452, 453. The CPU 411 thus can adaptively controlgeneral coordination of the robot apparatus 101. Moreover, the CPU 411controls the attitude and operation of the robot apparatus 101 so thatthe ZMP position constantly moves toward the center of a ZMP stablearea.

The action control module 400 sends the processing state, that is, theextent to which the action corresponding to the will decided by thethought control module 300 was exhibited, to the thought control module300. In this manner, the robot apparatus 101 can judge the states ofitself and its surroundings on the basis of the control program and canact autonomously.

For such a robot apparatus, a human interface technique is required thatenables the robot apparatus to respond within a predetermined timeperiod in a dynamically changing work environment. As theabove-described face detection and facial expression recognitiontechniques are applied to the robot apparatus 101 according to thisembodiment, the robot apparatus 101 can identify the facial expressionsof users in the surroundings (owner, his/her friends, or authorizeduser) and control reactions based on the result of recognition (that is,in accordance with the users). Therefore, a high entertainment propertycan be realized.

This invention is not limited to the above-described embodiment andvarious changes and modifications can be made without departing from thescope of this invention. One or more arbitrary processing of theabove-described learning processing, face detection processing, facialexpression learning processing and facial expression recognitionprocessing in the above-described face detection apparatus may berealized by hardware or by causing an arithmetic unit (CPU) to executecomputer programs. In the case of using computer programs, the programsrecorded on a recording medium can be provided or the programs can beprovided by transmission via the Internet or other transmission media.

(10) Example

Now, an example of the facial expression recognition system described inthe above-described embodiment will be described in detail withreference to the results of actual experiment in the facial expressionrecognition system.

(10-1) Face Detection

(10-1-1) Training Data

First, the inventors of this application used Cohn and Kanade's DFAT-504data set (T. Kanade, J. F. Cohn, and Y. Tian, Comprehensive database forfacial expression analysis. In Proceedings of the 4^(th) internationalconference on automatic face and gesture recognition (FG'00), pages46-53, Grenoble, France, 2000), as learning samples for the facialexpression recognition system. The face detection apparatus was trainedand tested (evaluated) on this data set. The data set consists of 100university students ranging in age from 18 to 30 years. 65% were female,15% were African-American, and 3% were Asian or Latino.

Videos were recorded in analog S-video using a camera located directlyin front of the subject. Subjects were instructed by an experimenter toperform a series of 23 facial expressions. Subjects began and ended eachdisplay with a neutral face. Before performing each display, anexperimenter described and modeled the desired display.

Of the face images thus acquired, image sequences from neutral to targetdisplay were digitized into 640×480 pixel arrays with 8-bit precisionfor grayscale values.

In this example, 313 sequences were selected form the data set. The onlyselection criterion was that a sequence should be labeled as one of thesix basic emotions (basic expressions), that is, anger, hatred, fear,happiness, sadness, and surprise. The sequences came from 90 subjects,with one to six emotions per subject. The first and last frames (neutraland peak) were used as training images and for testing generalization tonew subjects, for a total of 625 data. The trained classifiers werelater applied to the entire sequence.

(10-1-2) Location of Faces

The face detection apparatus can scan all possible 24×24 pixel patches(windows) in the image and classify each as face or non-face in realtime. In order to detect face images of arbitrary sizes, the scale ofthe patches in the input image are converted using a scale factor of1.2. In the case where the detected patches have a significant overlap,these patches are averaged together as a detection window. The learningmethod for the face detection apparatus of this example will now bedescribed.

First, the face detection apparatus was trained on 5000 face imagesamples (face patches) and 10000 non-face image samples (non-facepatches) from about 8000 images collected from the web.

In a 24×24 pixel patch, there are over 160,000 possible filters, asdescribed above. In this example, a subset (filter group) of 2 to 200filters was selected from these 160,000 filters. Since the integralimages shown in FIG. 5 are used for calculation of the filters,high-speed calculation of rectangular boxes can be carried out.

To improve the calculation efficiency further, the filters were selectedby the method described in the above-described embodiment. Specifically,5% of all the possible filters were randomly selected, and one filterhaving the best face discrimination performance that minimizes theweighted classification error on the sample was selected. Then, a filtermade by shifting the selected filter by two pixels in each direction, afilter made by scaling the selected filter, and filters made byreflecting each shifted and scaled filter horizontally about the center(vertical bisector) of the image and superimposing it on the original,were generated. Of the selected filter and the newly generated filters,one filter with the best performance that minimizes the weightedclassification error on the sample was selected, and the single-filterclassifier was thus trained as a weak classifier (or “weak learner”) forface discrimination.

This can be thought of as a single-generation genetic algorithm. Usingthis, a filter of equivalent performance can be selected much fasterthan exhaustively searching for the best classifier among all 160,000possible filter and their reflection-based equivalents.

Using the selected classifier as the weak learner for boosting, theweights on the data were adjusted according to its performance on eachdata using the Adaboost rule.

This feature selection process was repeated with the new weights, andthe entire boosting procedure was continued until the “strongclassifier” (i.e., the combined classifier using all the weak learnersfor that stage) could achieve a minimum desired performance rate on adata set.

Finally, after training each strong classifier, a boot-strap round wasperformed (Kah Kay Sung and Tomaso Poggio, Example based learning forview-based human face detection, IEEE Trans. Pattern Anal. Mach.Intelligence, 20: 3951, 1998).

In this boot-strap round, the whole apparatus up to that point wasscanned across a database of non-face images, and false alarms (imageson which discrimination was incorrect) were collected and used as thenon-faces for training the subsequent strong classifier in the sequence.

While Adaboost is used in the feature selection algorithm in theconventional example 1, which requires binary classifiers, an experimentwas conducted in this example using “Gentleboost” to output realfunctions as outputs of weak discriminators as described in theabove-described embodiment (J. Friedman, T. Hastie, and R. Tibshirani,Additive logistic regression: A statistical view of boosting, ANNALS OFSTATISTICS, 28(2): 337-374, 2000). FIGS. 25A and 26A show the first twofilters selected by the apparatus that learns in accordance withGentleboost. FIGS. 25B and 26B show real-valued outputs (or tuningcurves) of the weak learners on all the samples acquired by thesefilter, that is, on the average face.

On the tuning curves, a large value on the vertical axis indicates aface and a small value indicates a non-face. The first tuning curveshown in FIG. 25B shows that a white rectangular box over a blackhorizontal region (rectangular box) in the center of the window isevidence of a face, and for non-face otherwise. That is, a valueacquired by subtracting the sum of brightness values in the lower blackrectangular box from the sum of brightness values in the upper whiterectangular box is the filter output, and an image on which the filteroutput is negative is a face image.

The second tuning curve shown in FIG. 26B shows bimodal distribution.Both the left and right rectangle features are the results ofsubtraction of the sum of brightness values in the outer rectangular boxfrom the sum of brightness values in the inner rectangular box.

Both rectangle features 34A, 34B show that the filter output ispositive, for example, for black hair, and negative for white hair. Animage on which there is no change in brightness value across therectangular boxes (the filter output is close to zero) in the rectanglefeatures 34A, 34B, is a non-face.

Moreover, the inventors of this application discovered a method foreliminating the cascade of classifiers as in the conventional example 1.That is, the output results of the weak discriminators are sequentiallyjudged and whether or not to continue the processing is decided. This isthe technique of judging whether the output of each single weakdiscriminator is less than the abort threshold value or not after theoutput of each weak discriminator is made, and stopping discrimination(feature test) in the next weak discriminator if the output is less thanthe abort threshold value, as described above. As a result ofpreliminary testing conducted by the inventors of this application, thespeed was dramatically improved with no loss of accuracy over thecurrent apparatus.

The strong classifiers early in the sequence (the combined classifiersusing all the weak classifiers for that stage) need very few features toachieve good performance. For example, the first stage can reject 60% ofthe non-faces, using only two features and using only 20 simpleoperations or about 60 microprocessor instructions. Therefore, theaverage number of features that need to be judged for each window isvery small, making the overall processing in the apparatus very fast.The face detection apparatus of this example can achieve very high speedas well as very high accuracy.

In the face detection apparatus in this example, performance on astandard, public data set for benchmarking a frontal face detectionapparatus such as the CMU-MIT data set was comparable to theabove-described conventional example 1. While the data set used for thisexample contains wide variability in the images due to illumination,occlusions, and differences in image quality, the performance was muchmore accurate on the data set used for learning in this example, becausethe faces were frontal, focused and well lit, with simple background.All faces were detected for this data set.

(10-2) Facial Expression Recognition

(10-2-1) Preprocessing

Next, the automatically located faces were rescaled to 48×48 pixels. Acomparison was also made at double resolution (faces rescaled to 96×96pixels). The typical distance between the centers of the eyes wasroughly 24 pixels. These rescaled images were converted into a Gabormagnitude representation, using a bank of Gabor filters at eightorientations and five spatial frequencies (4:16 pixels per cycle at ½octave steps).

(10-2-2) Facial Expression Classification

Facial expression classification was based on support vector machines(SVMs). SVMs are suited to this task because the high dimensionality ofthe Gabor representation does not affect training time for kernelclassifiers (facial expression identifiers). The facial expressionclassifiers performed a 7-way forced choice between the followingemotion categories: happiness, sadness, surprise, disgust, fear, anger,and neutral.

The classification was performed in two stages. First, support vectormachines performed binary decision tasks. Seven SVMs were trained todiscriminate each emotion from everything else. The emotion categorydecision was then implemented by choosing the classifier that providedmaximum margin for the data of the detection target expression. Aslinear, polynomial, and RBF kernels with Laplacian and Gaussian basisfunctions were explored, linear and RBF kernels employing a unit-widthGaussian performed best. The examples using linear and RBF kernels willnow be described.

The inventors of this application compared expression recognitionperformance using the output of the above-described automatic facedetection apparatus, with expression recognition performance on imageswith explicit feature alignment using hand-labeled features. For themanually aligned face images, the faces were rotated so that the eyeswere horizontal and then warped so that the eyes and mouth were alignedin each face.

Generalization to novel subjects was tested using leave-one-sample-outcross validation. The results are given in the following Table 1. Theseresults are on 96×96 pixel samples.

TABLE 1 SVM Automatic Manually aligned Linear kernels 84.8 85.3 RBFkernels 87.5 87.6

As shown in Table 1, there was no significant difference betweenexpression recognition performance on the automatically detected facesand expression recognition performance on the manually aligned faces(z=0.25, p=0.4).

(10-3) Comparison of SVMs and Adaboost

Next, performance of the emotion classifier (expression identifier) thatperforms expression recognition based on SVMs was compared withperformance of an emotion classifier using Adaboost.

The Adaboost emotion classifier used Gabor filter outputs. There were48×48×40=92160 possible features. A subset of these filters was selectedusing Adaboost. On each training (learning) round of repetitiveprocessing, the threshold value and scale parameter of each filter wereoptimized and the feature (Gabor filter) that provided the bestperformance on the boosted data weight distribution was selected.

In evaluation at the time of learning, since Adaboost is significantlyslower to train than SVMs, “leave-one-subject-out” cross validation(hereinafter referred to as leave-one-sample-out method) was not carriedout. Instead, the learning samples were separated randomly into tengroups of roughly equal size and “leave-one-group-out” cross validation(hereinafter referred to as leave-one-group-out method) was carried out.

In the leave-one-sample-out method, all the samples except for one areused for learning and the excluded one sample is used for learningevaluation, and this is performed for the number of samples. In theleave-one-group-out method, all the samples except for one group ofsamples are used for learning and the excluded one group is used forlearning evaluation, and this is performed for the number of groups.

In Adaboost, training for each emotion classifier continued until thedistributions for the positive and negative samples were completelyseparated by a gap proportional to the widths of the two distributions.The total number of filters selected using this procedure was 538.

FIG. 27A is a graph showing output of one expression classifier duringAdaboost training. FIG. 27B is a graph showing generalization error as afunction of the number of features selected by Adaboost. Response toeach of training data is shown as a function of the number of featuresin accordance with improvement in skill of the classifier. Stoppingcriteria for Adaboost training can be thus found. The generalizationerror did not increase with “overtraining”.

This apparatus calculated the output of Gabor filters less efficientlybecause the convolutions were done in pixel space rather than Fourierspace, but the use of 200 times fewer. Gabor filters neverthelessenabled sufficient expression identification and thus realized asubstantially high speed. The following Table 2 shows comparison ofperformance of Adaboost, SVMs, and AdaSVMs (48×48 images). As shown inTable 2, the generalization performance of Adaboost was 85.0%, which wascomparable to linear SVM performance on the leave-one-group-out testingparadigm, but Adaboost was substantially faster, as shown in thefollowing Table 3. Table 3 shows the result of processing time andmemory considerations.

Adaboost provides an added value of choosing which features (filters)are most informative to test at each round of repetitive learning forweak discriminators. FIG. 28 shows the first five Gabor filters (Gaborfeatures) selected for each emotion. That is, FIG. 28 shows the outputresults of the first five filters with their frequencies andorientations sequentially selected in accordance with the Adaboostalgorithm, for each of the expression identifiers corresponding toanger, disgust, fear, happiness, sadness, and surprise.

In FIG. 28, white dots indicate pixel positions of all the Gaborfeatured selected by learning. Below the face image of each expression,a linear combination of the real part of the first five Adaboostfeatures selected for that expression is shown.

FIG. 29 is a graph showing wavelength distribution of the featuredselected by Adaboost, with respect to the five frequencies used for theGabor filters. In FIG. 29, the selected Gabor features show nopreference for direction, but the wavelengths of the highest frequenciesare selected more often.

(10-4) AdaSVMs

Moreover, the inventors of this application used a combination approach(AdaSVMs), in which the Gabor features selected by Adaboost were used asa reduced representation for training SVMs. This AdaSVMs outperformedAdaboost by 3.8 percent points. This was a statistically significantdifference (z=1.99, p=0.02). AdaSVMs outperformed SVMs by an average of2.7 percent points (z=1.55, p=0.06).

As shown in FIG. 29, as the inventors of this application examined thefrequency distribution of the Gabor filters selected by Adaboost, itbecame apparent that Gabor filters of higher spatial frequency andimages of higher resolution images could potentially improve performanceof the emotion classifiers. Doubling the resolution of images to 96×96pixels and increasing the number of Gabor wavelengths from 5 to 9 sothat they spanned 2:32 pixels in ½ octave steps, improved performance ofthe nonlinear AdaSVMs to 93.3%. As the resolution increased, the speedbenefit of AdaSVMs became even more apparent. At the highest resolution,the full Gabor representation increased by a factor of 7, whereas thenumber of Gabor filters selected by Adaboost only increased by a factorof 1.75.

TABLE 2 Leave-group-out Leave-subject-out Adaboost SVM SVM AdaSVM Linear85.0 84.8 86.2 88.8 RBF 86.9 88.0 90.7

TABLE 3 SVM AdaSVM Linear RBF Adaboost Linear RBF Time t t 90t 0.01t0.01t 0.0125t Time t′ t 90t 0.16t 0.16t 0.2t Memory m 90m 3m 3m 3.3m

In Table 3, time t′ includes the extra time to calculate the outputs ofthe 538 Gabor filters in pixel space for Adaboost and AdaSVMs, ratherthan the full FFT employed by the SVMs.

(10-5) Real-Time Emotion Mirroring

Although each individual image inputted to the emotion classifier isseparately processed and classified, the output of the apparatus for asequence of video frames changes smoothly as a function of time. FIGS.30A and 30B show two test sequences for one learning sample (sample 32).FIG. 30A shows the output result of the emotion classifier thatidentifies the emotion of “anger”. FIG. 30B shows the output result ofthe emotion classifier that identifies the emotion of “disgust”. Asshown in FIGS. 30A and 30B, the neutral output decreases and the outputfor the relevant emotion increases as a function of time. This providesa potentially valuable representation to code facial expressions in realtime.

To demonstrate the potential effect of real-time coding of facialexpressions, the inventors of this application developed a real-time“emotion mirror” device. The emotion mirror device is adapted fordisplaying a 3D character in real time that mimics the emotionalexpression of a person.

FIG. 31 shows exemplary outputs of the emotion mirror device utilizingthe facial expression recognition system according to the example ofthis invention. The animated character on the right side mirrors thefacial expression of the user.

The emotion mirror device comprises a face detector, an emotionclassifier, and an animation generator. The face detector detects a faceimage of the user and sends it to the emotion classifier. The emotionclassifier in this example employed the linear AdaSVM. The outputs ofthe emotion classifier that classifies emotions into seven categoriesconstitute a 7-D emotion code. This emotion code was sent to theanimation generator. The animation generator is a software tool fordisplaying 3D computer animated character images in real time. The 7-Demotion code gave a weighted combination of morph targets for eachemotion.

The inventors of this application also demonstrated, at NIPS 2002, aprototype of the emotion mirror device that recognized the emotion ofthe user and responded in an engaging way.

With this device, the present system can be incorporated into roboticand computer applications in which it is important to engage the user atan emotional level and have the computer recognize and adapt to theemotions of the user.

The use of the present system is currently considered at homes, schoolsand in laboratory environments. For example, at schools, the system canbe used as an automated tutoring system adapted to the emotional andcognitive state of the student. Moreover, automatic face tracking andexpression analysis are getting integrated into automatic animatedtutoring systems. Such automated tutoring systems may be more effectiveif they adapt to the emotional and cognitive state of the student, likereal teachers do. Face detection and expression recognition may makerobot apparatuses more attractive to users. This system also provides amethod for measuring the goodness of interaction between humans androbots. The inventors of this application measured the response of theuser during interaction with the robot apparatus, using the automaticexpression recognition system of this example. Whether or not theexpression recognition function enhances user enjoyment with the robotapparatus can be thus evaluated.

The expression recognition system in this example can performuser-independent and fully automatic coding of expressions. At least forapplications in which frontal views are assumed, it enables real-timerecognition of facial expressions with the existing computer power. Theproblem of classification into seven basic expressions can be solvedwith high accuracy by a simple linear system, using outputs of a bank ofGabor filters filtered from face images by preprocessing. The use ofSVMs for this identification enables highly accurate classification. Theresults of this example are consistent with those reported by Padgettand Cottrell on a smaller data set (C. Padgett and G. Cottrell,Representing face images for emotion classification. In M. Mozer, M.Jordan, and T Petsche, editors, Advances in Neural InformationProcessing Systems, volume 9, Cambridge, Mass., 1997, MIT Press). Forexample, a conventional system described in M. Lyons, J. Budynek, A.Plante, and S. Akamatsu, Classifying facial attributes using a 2d gaborwavelet representation and discriminant analysis, In Proceedings of the4^(th) international conference on automatic face and gesturerecognition, pages 202-207, 2000, employed discriminant analysis (LDA)to classify facial expressions from Gabor representations.

On the other hand, the inventors of this application tried SVMs forfacial expression classification. While LDA is optimal when the classdistributions are Gaussian, SVMs may be more effective when the classdistributions are not Gaussian.

Good performance results were obtained for directly processing theoutput of an automatic face detection apparatus without the need forexplicit detection and registration of facial features. Emotionidentification performance of a nonlinear SVM on the output of theautomatic face detection apparatus was almost identical to emotionidentification performance on the same set of faces using explicitfeature alignment with hand-labeled features.

Using Adaboost to perform feature selection greatly speeded up theapplication. Moreover, SVMs that were trained using features selected byAdaboost showed improved classification performance over Adaboost.

While the invention has been described in accordance with certainpreferred embodiments thereof illustrated in the accompanying drawingsand described in the above description in detail, it should beunderstood by those ordinarily skilled in the art that the invention isnot limited to those embodiments, but various modifications, alternativeconstructions or equivalents can be implemented without departing fromthe scope and spirit of the present invention as set forth and definedby the appended claims.

1. A learning apparatus for learning data to be used by a detection apparatus, the detection apparatus being adapted for judging whether provided data is a detection target or not by using a data set including plural learning samples each of which has data weighting set thereon and has been labeled as a detection target or non-detection target, the learning apparatus comprising: one or more programmable central processing units, and a computer-readable storage medium encoded with instructions executable by at least one of the central processing units and operatively coupled to at least one or the central processing units, the instructions comprising instructions that comprise a weak hypothesis generation unit for generating a weak hypothesis for estimating whether provided data is a detection target or not, instructions that comprise a reliability calculation unit for calculating reliability of the weak hypothesis on the basis of the result of estimation of the weak hypothesis generated by the weak hypothesis generation unit with respect to the data set, and instructions that comprise a data weighting update unit for updating the data weighting in such a manner that the data weighting of a learning sample on which estimation by the weak hypothesis generated by the weak hypothesis generation unit is incorrect becomes relatively larger than the data weighting of a learning sample on which estimation is correct; wherein the weak hypothesis generation unit comprises a selection unit for selecting a part of plural weak hypotheses and selecting one or plural weak hypotheses having higher estimation performance with respect to the data set from the selected part of the weak hypotheses, as high-performance weak hypotheses, a threshold value learning unit for calculating and adding the product of the result of estimation of the weak hypothesis with respect to the data set and the reliability of the weak hypothesis every time a weak hypothesis is selected by the weak hypothesis selection unit and learning an abort threshold value for aborting the processing by the detection apparatus to judge whether the provided data is a detection target or not on the basis of the result of the addition, a new weak hypothesis generation unit for generating one or more new weak hypotheses by adding a predetermined modification to the high-performance weak hypotheses, and a weak hypothesis selection unit for selecting one weak hypothesis having the highest estimation performance with respect to the data set from the high-performance weak hypotheses and the new weak hypotheses, the weak hypothesis generation unit repeating processing to generate a weak hypothesis every time the data weighting is updated by the data weighting update unit; and wherein the threshold value learning unit learns the abort threshold value on the basis of the result of addition of the product of the result of estimation of the weak hypothesis with respect to positive data labeled as the detection target, of the data set, and the reliability of the weak hypothesis, calculated and added every time a weak hypothesis is selected by the weak hypothesis selection unit.
 2. A learning apparatus for learning data to be used by a detection apparatus, the detection apparatus being adapted for judging whether provided data is a detection target or not by using a data set including plural learning samples each of which has been labeled as a detection target or non-detection target, the learning apparatus comprising: one or more programmable central processing units; and a computer-readable storage medium encoded with instructions executable by at least one of the central processing units and operatively coupled to at least one or the central processing units, the instructions comprising instructions that comprise a weak hypothesis selection unit for repeating processing to select one weak hypothesis from plural weak hypotheses for estimating whether provided data is a detection target or not, instructions that comprise a reliability calculation unit for, every time a weak hypothesis is selected by the weak hypothesis selection unit, calculating reliability of the weak hypothesis on the basis of the result of estimation of the selected weak hypothesis with respect to the data set, and instructions that comprise a threshold value learning unit for calculating and adding the product of the result of estimation of the weak hypothesis with respect to the data set and the reliability of the weak hypothesis every time a weak hypothesis is selected by the weak hypothesis selection unit and learning an abort threshold value for aborting the processing by the detection apparatus to judge whether the provided data is a detection target or not on the basis of the result of the addition.
 3. The learning apparatus as claimed in claim 2, wherein: the computer-readable storage medium is encoded with instructions that comprise a data weighting update unit for, every time the weak hypothesis is selected, updating the data weighting in such a manner that the data weighting of a learning sample on which estimation by the selected weak hypothesis is incorrect becomes relatively larger than the data weighting of a learning sample on which estimation is correct, and the weak hypothesis selection unit repeats processing to select the weak hypothesis every time the data weighting is updated.
 4. The learning apparatus as claimed in claim 2, wherein the threshold value learning unit learns the abort threshold value on the basis of the result of addition of the product of the result of estimation of the weak hypothesis with respect to positive data labeled as the detection target, of the data set, and the reliability of the weak hypothesis, calculated and added every time a weak hypothesis is selected by the weak hypothesis selection unit.
 5. The learning apparatus as claimed in claim 4, wherein the threshold value learning unit stores a smaller one of a minimum value of the result of addition with respect to the positive data and a discrimination boundary value, as the abort threshold value, every time the weak hypothesis is selected.
 6. The learning apparatus as claimed in claim 2, wherein the threshold value learning unit learns the abort threshold value on the basis of the result of addition of the product of the result of estimation of the weak hypothesis with respect to negative data labeled as the non-detection target, of the data set, and the reliability of the weak hypothesis, calculated and added every time a weak hypothesis is selected by the weak hypothesis selection unit.
 7. The learning apparatus as claimed in claim 6, wherein the threshold value learning unit stores a larger one of a maximum value of the result of calculation with respect to the negative data and a discrimination boundary value, as the abort threshold value, every time the weak hypothesis is selected.
 8. A learning method for learning data to be used by a detection apparatus, the detection apparatus being adapted for judging whether provided data is a detection target or not by using a data set including plural learning samples each of which has been labeled as a detection target or non-detection target, the learning method being performed by an apparatus that comprises one or more programmable central processing units and a computer-readable storage medium that is operatively coupled to at least one of the central processing units and is encoded with instructions capable of being executed by at least one of the central processing units, the method comprising: at least one of the central processing units executing instructions, retrieved from the computer-readable storage medium, that cause the central processing unit to perform a weak hypothesis selection step of repeating processing to select one weak hypothesis from plural weak hypotheses for estimating whether provided data is a detection target or not; at least one of the central processing units executing instructions, retrieved from the computer-readable storage medium, that cause the central processing unit to perform a reliability calculation step of, every time a weak hypothesis is selected at the weak hypothesis selection step, calculating reliability of the weak hypothesis on the basis of the result of estimation of the selected weak hypothesis with respect to the data set; and at least one of the central processing units executing instructions, retrieved from the computer-readable storage medium, that cause the central processing unit to perform a threshold value learning step of calculating and adding the product of the result of estimation of the weak hypothesis with respect to the data set and the reliability of the weak hypothesis every time a weak hypothesis is selected at the weak hypothesis selection step, and learning an abort threshold value for aborting the processing by the detection apparatus to judge whether the provided data is a detection target or not on the basis of the result of the addition. 